IEEE Symp Research Articles

(Invited) Epitaxial Growth and Development of Complimentary Field-Effect Transistors

The semiconductor industry is currently at a pivotal juncture, with major chip fabrication facilities having exhausted FINFET technology and now transitioning to a new device architecture of gate all around (GAA). The next architecture in this progression (beyond 1nm), crucial for scaling down is Complementary Field-Effect Transistors (cFETs). In cFETs, nMOS and pMOS are stacked on top of each other, eliminating the gap and resulting in significant reduction of area and maximization of channel width and drive current.[1-3] In this work, we present our research on epitaxial growth of cFET stacks and discuss our design strategies and the key evaluation metrics in accordance with the downstream processes. We delve deeper into the bottom-up growth of cFETs using Chemical Vapor Deposition (CVD) epitaxy and explore the impact of temperature, precursor gases, and Germanium content on the quality and strain engineering of cFETs. We exploit various characterization techniques to quantify defects, strain, uniformity, and composition of the epitaxial layers comprising the cFET stacks, followed by tuning of the process parameters accordingly to achieve a high-quality, fully-strained stack. Through this study, we aim to provide valuable insights into the growth and optimization of cFET structures, thereby facilitating their integration into future transistor nodes.[1] P. Schuddincket al., 2022 IEEE Symp. on VLSI Techn. & Circuits, Digest of Technical Papers, p. 365.[2] S. Subramanian et al., 2020 IEEE Symp. on VLSI Techn. & Circuits, Digest of Technical Papers, TH3.1.[3] A. Vandooren et al., 2022 IEEE Symp. on VLSI Techn. & Circuits, Digest of Technical Papers, p. 330.

Evaluation of Anisotropic Biaxial Stress in Extremely-Thin Body (100) Silicon-Germanium-on-Insulator p-Type Metal-Oxide-Semiconductor Field-Effect-Transistor by Oil-Immersion Raman Spectroscopy

Background and ObjectiveSilicon germanium (SiGe)-on-insulator (SGOI) p-MOSFETs are expected for obtaining low power consumption and high current drive of CMOS since SiGe has higher hole career mobility than Si and the compressive strain can be induced in the SiGe channel without complicated heterostructures. In addition, the buried oxide between the Si substrate and the SiGe layer realizes suppression of leak current, and an extremely thin body (ETB) SGOI prevents short-channel effects. Strain engineering is important for improving the performance of p-MOSFETs because the hole mobility increases due to the compressive strain in the channel region. In previous studies, we have reported that anisotropic strain in ETB GOI channels of p-MOSFET improved electrical properties [1]. However, there are few reports regarding the detailed stress evaluation in ETB SGOI p-MOSFETs. The strain state has changed complicatedly by the SiGe device process. Therefore, a detailed stress measurement is indispensable to determine career mobility enhancement in the actual channel fabrication. In this study, we evaluated the anisotropic biaxial stress in the channel region of the ETB (100) SGOI p-MOSFETs by oil-immersion Raman spectroscopy.Experiments We prepared (100) SGOI p-MOSFETs along <110> with a channel thickness of approximately 10 nm by applying the Ge condensation process with slow cooling on the 60 nm-thick Si0.75Ge0.25 films epitaxially grown on SOI substrates with 10 nm-thick superficial Si layer [2]. We used the Ge condensation process that combined oxidation and intermixing annealing in order to suppress strain relaxation in the Ge-rich region [3] and obtained Ge-rich SiGe layer (Ge fraction: from 65 to 70%). For the evaluation of anisotropic biaxial stress in the SiGe channel region, we measured longitudinal optical (LO) and transverse optical (TO) phonon modes of Raman spectra for Ge-Ge vibration mode derived from SiGe by using oil-immersion Raman spectroscopy. In the oil-immersion Raman measurements, the wavelength of the excitation light source was 532 nm, the laser power at the sample surface was less than 1 mW, and the focal length of the spectrometer was 2,000 mm. The numerical aperture of the oil-immersion lens was 1.4, and the reflective index of oil was 1.5. We measured p-MOSFETs with different channel widths to examine the channel width dependence.Results and DiscussionFigure 1(a) and (b) show the Raman spectra of the LO and TO phonon modes obtained from the SiGe channel region at channel width (Wch) = 738 nm, respectively. We observed that Raman peaks of LO phonon mode shifted toward the higher wavenumber side compared to the Raman peak of strain-free SiGe. These results suggest that the high compressive strain is induced in the SiGe channel.Figure 1(c) shows the calculated transverse stress (σxx) and longitudinal stress (σyy) of the samples using LO and TO Raman shift for four different channel widths under the assumption of the anisotropic biaxial stress and Ge fraction 68% in the SiGe layer. From Fig. 1(c), we observed transverse stress (σxx) decreases with narrowing channel width. On the other hand, the longitudinal stress (σyy) did not significantly change regardless of channel width. These results suggest that the strain states in the SiGe channel region became closer to the uniaxial strain with narrowing the channel width. These changes are in good agreement with the previous electrical characteristics studies of the GOI p-MOSFETs [1], and it is expected that the compressive strain enhances the hole mobility in the ETB SGOI p-MOSFETs as well.AcknowledgementsThis work was supported by JSPS KAKENHI Grant Number 22H00208, Japan. A part of this work was conducted at Takeda Sentanchi Supercleanroom, The University of Tokyo, supported by "Nanotechnology Platform Program" of MEXT, Japan, Grant Number JPMXP09F-20-UT-0007. Reference [1] C. -T. Chen et al., IEEE Trans. Electron Devices 69, 1 (2022).[2] C. -T. Chen et al., Proc. IEEE Symp. VLSI Technology (2021).[3] K. -W. Jo et al., Appl. Phys. Lett. 114, 062101 (2019). Figure 1

List-Decoding with Double Samplers

We strengthen the notion of double samplers, first introduced by Dinur and Kaufman [``High dimensional expanders imply agreement expanders,” in Proc. 58th IEEE Symp. on Foundations of Comp. Science, IEEE, 2017, pp. 974--985], which are samplers with additional combinatorial properties, and whose existence we prove using high-dimensional expanders. The ABNNR code construction [N. Alon et al., IEEE Trans. Inform. Theory, 38 (1992), pp. 509--516] achieves large distance by starting with a base code $C$ with moderate distance, and then amplifying the distance using a sampler. We show that if the sampler is part of a larger double sampler, then the construction has an efficient list-decoding algorithm. Our algorithm works even if the ABNNR construction is not applied to a base code $C$ but rather to any string. In this case the resulting code is approximate-list-decodable, i.e., the output list contains an approximation to the original input. Our list-decoding algorithm works as follows: It uses a local voting scheme from which it constructs a unique games constraint graph. The constraint graph is an expander, so we can solve unique games efficiently. These solutions are the output of the list-decoder. This is a novel use of a unique games algorithm as a subroutine in a decoding procedure, as opposed to the more common situation in which unique games are used for demonstrating hardness results. Double samplers and high-dimensional expanders are akin to pseudorandom objects in their utility, but they greatly exceed random objects in their combinatorial properties. We believe that these objects hold significant potential for coding theoretic constructions and view this work as demonstrating the power of double samplers in this context.

Electronic and Optical Properties of Short-Period Si/Sige Superlattices: Effects of Interfacial Atomic-Scale Roughness

SiGe/Si superlattice (SL) are currently a central building block of nanosheet transistors proposed for the 7 nm technology nodes and beyond [1], where elective wet-etching of the SiGe layers has been used to release the Si layers and form a vertically stacked channels architecture [2]. Consequently, the interfacial abruptness and uniformity in heterostructures are critical to control their electronic and optical properties. Recently, we demonstrated a 3-D atomistic-level mapping of the roughness and uniformity of buried epitaxial interfaces in Si/SiGe SLs with a layer thickness in the 1.5-7.5 nm range [3]. This direct quantification of the abruptness of buried interfaces enabled a direct evaluation of interfacial effects on electronic and optical properties of epitaxial heterostructures. For instance, spectroscopic ellipsometry indicated the first observation of a new superlattice-related optical transition between 2.2 and 2.7 eV. However, the interpretation of this new transition can only be achieved using a theoretical framework considering atomic-level details of the interfacial roughness. To that end, we have been carrying out theoretical investigations to build a correct quantum mechanical model that incorporates the effect of the interface, directly measured from atom probe tomography (APT), to interpret the possible SL-related optical transition. Thus, an 8-band k⋅p formalism was developed and validated for group IV semiconductors [4], where a quantum mechanical incorporation of the interface width is highly coveted because the microscopic interface asymmetry (MIA) effect can greatly influence the electronic and optical properties of short-period SLs, induce strong interactions between different SL subbands, and enhance the absorption strength considerably [5]. It has been shown that the nature of the SL interfaces can have a significative impact on the optical confinement properties of other group IV heterostructures [6]. To test this model, experimental optical characterization of four different SLs (the mean Ge concentration of the layers within the SLs is in the 25 to 30 at. % range and is the periodicity of the SLs) will be presented and discussed. Then, by simulating the SL optical properties with the developed 8-band k⋅p method, the effect of the interface will be investigated to try and explain the observed spectroscopic transition.[1] G. Hellings, et al, in 2018 IEEE Symp. VLSI Technol. (IEEE, 2018), pp. 85–86.[2] K. Komori, et al, Solid State Phenom. 282, 107 (2018).[3] S. Mukherjee, et al, ArXiv: Cond-Mat 1908.00874, 1 (2019).[4] T. B. Bahder, Phys. Rev. B 41, 11992 (1990).[5] H. M. Dong, et al, Thin Solid Films 589, 388 (2015).[6] F. Szmulowicz, et al, Phys. Rev. B - Condens. Matter Mater. Phys. 69, 155321 (2004).

An Ultralow-Power On-Die PMU in a 28-nm CMOS SoC With Direct Li-Ion Battery-Attach Capability

This paper introduces an on-die power management unit (PMU) within Blackghost 1.0—a test chip for Qualcomm’s newest Blackghost ultralow-power mixed-signal system-on-chip product family. Specifically targeted at battery-powered Internet-of-Things, wearables, and e-medical applications, Blackghost delivers unparalleled power efficiency through low-power innovations from software, architecture, and circuit design [Y. Pu et al., Proc. IEEE Symp. Low-Power High-Speed Chips (COOL CHIPS) , Apr. 2017, pp. 1–3]. It integrates a small footprint sensor/control processor based on ARM Cortex M0, an on-die PMU with direct Li-ion battery-attach capability, a computer vision classifier processor, a programmable DSP hardware accelerator, and an ultralow-power analog front end on a $3 \times 3$ mm2 die in the TSMC 28LP CMOS process technology. The on-die PMU consists of a bandgap reference, a low-frequency RC clock, a high-frequency RC clock, a low drop-out linear regulator, and two switch mode power supply (SMPS) buck regulators. It supports direct Li-ion battery-attach by accepting input voltages up to 5 V. The total quiescent current of the entire PMU is only $9~\mu \text{A}$ . Its SMPS maintains high efficiencies (around 80%) with load currents as low as $10~\mu \text{A}$ .

Spatial mixing and the connective constant: optimal bounds

We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model (which is defined as a weighted sum over all matchings where each matching is given a weight $$\gamma ^{|V| - 2 |M|}$$ in terms of a fixed parameter $$\gamma $$ called the monomer activity) and the hard core model (which is defined as a weighted sum over all independent sets where an independent set I is given a weight $$\lambda ^{|I|}$$ in terms of a fixed parameter $$\lambda $$ called the vertex activity). The connective constant is a natural measure of the average degree of a graph which has been studied extensively in combinatorics and mathematical physics, and can be bounded by a constant even for certain unbounded degree graphs such as those sampled from the sparse Erdős–Renyi model $$\mathcal {G}(n, d/n)$$ . Our main technical contribution is to prove the best possible rates of decay of correlations in the natural probability distributions induced by both the hard core model and the monomer-dimer model in graphs with a given bound on the connective constant. These results on decay of correlations are obtained using a new framework based on the so-called message approach that has been extensively used recently to prove such results for bounded degree graphs. We then use these optimal decay of correlations results to obtain fully polynomial time approximation schemes (FPTASs) for the two problems on graphs of bounded connective constant. In particular, for the monomer-dimer model, we give a deterministic FPTAS for the partition function on all graphs of bounded connective constant for any given value of the monomer activity. The best previously known deterministic algorithm was due to Bayati et al. (Proc. 39th ACM Symp. Theory Comput., pp. 122–127, 2007), and gave the same runtime guarantees as our results but only for the case of bounded degree graphs. For the hard core model, we give an FPTAS for graphs of connective constant $$\varDelta $$ whenever the vertex activity $$\lambda < \lambda _c(\varDelta )$$ , where $$\lambda _c(\varDelta ) :=\frac{\varDelta ^\varDelta }{(\varDelta - 1)^{\varDelta + 1}}$$ ; this result is optimal in the sense that an FPTAS for any $$\lambda > \lambda _c(\varDelta )$$ would imply that NP=RP (Sly and Sun, Ann. Probab. 42(6):2383–2416, 2014). The previous best known result in this direction was in a recent manuscript by a subset of the current authors (Proc. 54th IEEE Symp. Found. Comput. Sci., pp 300–309, 2013), where the result was established under the sub-optimal condition $$\lambda < \lambda _c(\varDelta + 1)$$ . Our techniques also allow us to improve upon known bounds for decay of correlations for the hard core model on various regular lattices, including those obtained by Restrepo et al. (Probab Theory Relat Fields 156(1–2):75–99, 2013) for the special case of $$\mathbb {Z}^2$$ using sophisticated numerically intensive methods tailored to that special case.

Authenticated Adversarial Routing

The aim of this paper is to demonstrate the feasibility of authenticated throughput-efficient routing in an unreliable and dynamically changing synchronous network in which the majority of malicious insiders try to destroy and alter messages or disrupt communication in any way. More specifically, in this paper we seek to answer the following question: Given a network in which the majority of nodes are controlled by a node-controlling adversary and whose topology is changing every round, is it possible to develop a protocol with polynomially bounded memory per processor (with respect to network size) that guarantees throughput-efficient and correct end-to-end communication? We answer the question affirmatively for extremely general corruption patterns: we only request that the topology of the network and the corruption pattern of the adversary leaves at least one path each round connecting the sender and receiver through honest nodes (though this path may change at every round). Out construction works in the public-key setting and enjoys optimal transfer rate and bounded memory per processor (that is polynomial in the network size and does not depend on the amount of traffic). We stress that our protocol assumes no knowledge of which nodes are corrupted nor which path is reliable at any round, and is also fully distributed with nodes making decisions locally, so that they need not know the topology of the network at any time. The optimality that we prove for our protocol is very strong. Given any routing protocol, we evaluate its efficiency (rate of message delivery) in the case, that is with respect to the worst possible graph and against the worst possible (polynomially bounded) adversarial strategy (subject to the above mentioned connectivity constraints). Using this metric, we show that there does not exist any protocol that can be asymptotically superior (in terms of throughput) to ours in this setting. We remark that the aim of our paper is to demonstrate via explicit example the feasibility of throughput-efficient authenticated adversarial routing. However, we stress that out protocol is not intended to provide a practical solution, as due to its complexity, no attempt thus far has been made to reduce constants and memory requirements. Our result is related to recent work of Barak et al. (Proc. of Advances in Cryptology--27th EUROCRYPT 2008, LNCS, vol. 4965, pp. 341---360, 2008) who studied fault localization in networks assuming a private-key trusted-setup setting. Our work, in contrast, assumes a public-key PKI setup and aims at not only fault localization, but also transmission optimality. Among other things, our work answers one of the open questions posed in the Barak et al. paper regarding fault localization on multiple paths. The use of a public-key setting to achieve strong error-correction results in networks was inspired by the work of Micali et al. (Proc. of 2nd Theory of Cryptography Conf., LNCS, vol. 3378, pp. 1---16, 2005) who showed that classical error correction against a polynomially bounded adversary can be achieved with surprisingly high precision. Our work is also related to an interactive coding theorem of Rajagopalan and Schulman (Proc. 26th ACM Symp. on Theory of Computing, pp. 790---799, 1994) who showed that in noisy-edge static-topology networks a constant overhead in communication can also be achieved (provided none of the processors are malicious), thus establishing an optimal-rate routing theorem for static-topology networks. Finally, our work is closely related and builds upon to the problem of End-To-End Communication in distributed networks, studied by Afek and Gafni (Proc. of the 7th ACM Symp. on Principles of Distributed Computing, pp. 131---148, 1988); Awebuch et al. (Proc. of the 30th IEEE Symp. on Foundations of Computer Science, FOCS, 1989); Afek et al. (Proc. of the 11th ACM Symp. on Principles of Distributed Computing, pp. 35---46, 1992); and Afek et al. (J. Algorithms 22:158---186, 1997), though none of these papers consider or ensure correctness in the setting of a node-controlling adversary that may corrupt the majority of the network.

On Core XPath with Inflationary Fixed Points

We prove the undecidability of Core XPath 1.0 (CXP) [G. Gottlob and C. Koch, inProc. of 17th Ann. IEEE Symp. on Logic in Computer Science, LICS ’02 (Copenhagen, July 2002).IEEE CS Press (2002) 189–202.] extended with anInflationary Fixed Point (IFP)operator. More specifically, we prove that the satisfiability problem of this language is undecidable. In fact, the fragment of CXP+IFP containing only theselfanddescendantaxes is already undecidable.

Average Rate Speed Scaling

Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao, Demers, and Shenker (Proc. IEEE Symp. Foundations of Computer Science, pp. 374–382, 1995) considered the problem where the QoS constraint is deadline feasibility and the objective is to minimize the energy used. They proposed an online speed scaling algorithm Average Rate (AVR) that runs each job at a constant speed between its release and its deadline. They showed that the competitive ratio of AVR is at most (2α) α /2 if a processor running at speed s uses power s α . We show the competitive ratio of AVR is at least ((2−δ)α) α /2, where δ is a function of α that approaches zero as α approaches infinity. This shows that the competitive analysis of AVR by Yao, Demers, and Shenker is essentially tight, at least for large α. We also give an alternative proof that the competitive ratio of AVR is at most (2α) α /2 using a potential function argument. We believe that this analysis is significantly simpler and more elementary than the original analysis of AVR in Yao et al. (Proc. IEEE Symp. Foundations of Computer Science, pp. 374–382, 1995).

Martingale families and dimension in P

We introduce a new measure notion on small complexity classes (called F -measure), based on martingale families, that gets rid of some drawbacks of previous measure notions: it can be used to define dimension because martingale families can make money on all strings, and it yields random sequences with an equal frequency of 0 ’s and 1 ’s. On larger complexity classes ( E and above), F -measure is equivalent to Lutz resource-bounded measure. As applications to F -measure, we answer a question raised in [E. Allender, M. Strauss, Measure on small complexity classes, with application for BPP, in: Proc. of the 35th Ann. IEEE Symp. on Found. of Comp. Sci., 1994, pp. 807–818] by improving their result to: for almost every language A decidable in subexponential time, P A = BPP A . We show that almost all languages in PSPACE do not have small non-uniform complexity. We compare F -measure to previous notions and prove that martingale families are strictly stronger than Γ -measure [E. Allender, M. Strauss, Measure on small complexity classes, with application for BPP, in: Proc. of the 35th Ann. IEEE Symp. on Found. of Comp. Sci., 1994, pp. 807–818], we also discuss the limitations of martingale families concerning finite unions. We observe that all classes closed under polynomial many-one reductions have measure zero in EXP iff they have measure zero in SUBEXP . We use martingale families to introduce a natural generalization of Lutz resource-bounded dimension [J.H. Lutz, Dimension in complexity classes, in: Proceedings of the 15th Annual IEEE Conference on Computational Complexity, 2000, pp. 158–169] on P , which meets the intuition behind Lutz’s notion. We show that P -dimension lies between finite-state dimension and dimension on E . We prove an analogue of a Theorem of Eggleston in P , i.e. the class of languages whose characteristic sequence contains 1 ’s with frequency α , has dimension the Shannon entropy of α in P .

Incremental Branching Programs

We propose a new model of restricted branching programs specific to solving GEN problems, which we call incremental branching programs. We show that syntactic incremental branching programs capture previously studied models of computation for the problem GEN, namely marking machines (Cook, S.A. in J. Comput. Syst. Sci. 9(3):308–316, 1974) and Poon’s extension (Proc. of the 34th IEEE Symp. on the Foundations of Computer Science, pp. 218–227, 1993) of jumping automata on graphs (Cook, S.A., Rackoff, C.W. in SIAM J. Comput. 9:636–652, 1980). We then prove exponential size lower bounds for our syntactic incremental model, and for some other variants of branching program computation for GEN. We further show that nondeterministic syntactic incremental branching programs are provably stronger than their deterministic counterpart when solving a natural NL-complete GEN sub-problem. It remains open if syntactic incremental branching programs are as powerful as unrestricted branching programs for GEN problems.

A faster distributed protocol for constructing a minimum spanning tree

This paper studies the problem of constructing a minimum-weight spanning tree ( MST) in a distributed network. This is one of the most important problems in the area of distributed computing. There is a long line of gradually improving protocols for this problem, and the state of the art today is a protocol with running time O ( Λ ( G ) + n ⋅ log ∗ n ) due to Kutten and Peleg [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27], where Λ ( G ) denotes the diameter of the graph G. Peleg and Rubinovich [D. Peleg, V. Rubinovich, A near-tight lower bound on the time complexity of distributed MST construction, in: Proc. 40th IEEE Symp. on Foundations of Computer Science, 1999, pp. 253–261] have shown that Ω ˜ ( n ) time is required for constructing MST even on graphs of small diameter, and claimed that their result “establishes the asymptotic near-optimality” of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. In this paper we refine this claim, and devise a protocol that constructs the MST in Ω ˜ ( μ ( G , ω ) + n ) rounds, where μ ( G , ω ) is the MST-radius of the graph. The ratio between the diameter and the MST-radius may be as large as Θ ( n ) , and, consequently, on some inputs our protocol is faster than the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27] by a factor of Ω ˜ ( n ) . Also, on every input, the running time of our protocol is never greater than twice the running time of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. As part of our protocol for constructing an MST, we develop a protocol for constructing neighborhood covers with a drastically improved running time. The latter result may be of independent interest.

Correlation clustering in general weighted graphs

We consider the following general correlation-clustering problem [N. Bansal, A. Blum, S. Chawla, Correlation clustering, in: Proc. 43rd Annu. IEEE Symp. on Foundations of Computer Science, Vancouver, Canada, November 2002, pp. 238–250]: given a graph with real nonnegative edge weights and a 〈 + 〉 / 〈 - 〉 edge labelling, partition the vertices into clusters to minimize the total weight of cut 〈 + 〉 edges and uncut 〈 - 〉 edges. Thus, 〈 + 〉 edges with large weights (representing strong correlations between endpoints) encourage those endpoints to belong to a common cluster while 〈 - 〉 edges with large weights encourage the endpoints to belong to different clusters. In contrast to most clustering problems, correlation clustering specifies neither the desired number of clusters nor a distance threshold for clustering; both of these parameters are effectively chosen to be the best possible by the problem definition. Correlation clustering was introduced by Bansal et al. [Correlation clustering, in: Proc. 43rd Annu. IEEE Symp. on Foundations of Computer Science, Vancouver, Canada, November 2002, pp. 238–250], motivated by both document clustering and agnostic learning. They proved NP-hardness and gave constant-factor approximation algorithms for the special case in which the graph is complete (full information) and every edge has the same weight. We give an O ( log n ) -approximation algorithm for the general case based on a linear-programming rounding and the “region-growing’’ technique. We also prove that this linear program has a gap of Ω ( log n ) , and therefore our approximation is tight under this approach. We also give an O ( r 3 ) -approximation algorithm for K r , r -minor-free graphs. On the other hand, we show that the problem is equivalent to minimum multicut, and therefore APX-hard and difficult to approximate better than Θ ( log n ) .

Efficiently computing succinct trade-off curves

Trade-off (aka Pareto) curves are typically used to represent the trade-off among different objectives in multiobjective optimization problems. Although trade-off curves are exponentially large for typical combinatorial optimization problems (and infinite for continuous problems), it was observed in Papadimitriou and Yannakakis [On the approximability of trade-offs and optimal access of web sources, in: Proc. 41st IEEE Symp. on Foundations of Computer Science, 2000] that there exist polynomial size ε approximations for any ε > 0 , and that under certain general conditions, such approximate ε -Pareto curves can be constructed in polynomial time. In this paper we seek general-purpose algorithms for the efficient approximation of trade-off curves using as few points as possible. In the case of two objectives, we present a general algorithm that efficiently computes an ε -Pareto curve that uses at most 3 times the number of points of the smallest such curve; we show that no algorithm can be better than 3-competitive in this setting. If we relax ε to any ε ′ > ε , then we can efficiently construct an ε ′ -curve that uses no more points than the smallest ε -curve. With three objectives we show that no algorithm can be c-competitive for any constant c unless it is allowed to use a larger ε value. We present an algorithm that is 4-competitive for any ε ′ > ( 1 + ε ) 2 - 1 . We explore the problem in high dimensions and give hardness proofs showing that (unless P=NP) no constant approximation factor can be achieved efficiently even if we relax ε by an arbitrary constant.

The black-box complexity of nearest-neighbor search

We define a natural notion of efficiency for approximate nearest-neighbor (ANN) search in general n-point metric spaces, namely the existence of a randomized algorithm which answers ( 1 + ɛ ) -ANN queries in polylog ( n ) time using only polynomial space. We then study which families of metric spaces admit efficient ANN schemes in the black-box model, where only oracle access to the distance function is given, and any query consistent with the triangle inequality may be asked. For ɛ < 2 5 , we offer a complete answer to this problem. Using the notion of metric dimension defined in [A. Gupta, et al., Bounded geometries, fractals, and low-distortion embeddings, in: 44th Annu. IEEE Symp. on Foundations of Computer Science, 2003, pp. 534–543] (à la [P. Assouad, Plongements lipschitziens dans R n , Bull. Soc. Math. France 111 (4) (1983) 429–448]), we show that a metric space X admits an efficient ( 1 + ɛ ) -ANN scheme for any ɛ < 2 5 if and only if dim ( X ) = O ( log log n ) . For coarser approximations, clearly the upper bound continues to hold, but there is a threshold at which our lower bound breaks down—this is precisely when points in the “ambient space” may begin to affect the complexity of “hard” subspaces S ⊆ X . Indeed, we give examples which show that dim ( X ) does not characterize the black-box complexity of ANN above the threshold. Our scheme for ANN in low-dimensional metric spaces is the first to yield efficient algorithms without relying on any additional assumptions on the input. In previous approaches (e.g., [K.L. Clarkson, Nearest neighbor queries in metric spaces, Discrete Comput. Geom. 22(1) (1999) 63–93; D. Karger, M. Ruhl, Finding nearest neighbors in growth-restricted metrics, in: 34th Annu. ACM Symp. on the Theory of Computing, 2002, pp. 63–66; R. Krauthgamer, J.R. Lee, Navigating nets: simple algorithms for proximity search, in: 15th Annu. ACM-SIAM Symp. on Discrete Algorithms, 2004, pp. 791–801; K. Hildrum, et al., A note on finding nearest neighbors in growth-restricted metrics, in: Proc. of the 15th Annu. ACM-SIAM Symp. on Discrete Algorithms, 2004, pp. 560–561]), even spaces with dim ( X ) = O ( 1 ) sometimes required Ω ( n ) query times.

On a simple randomized algorithm for finding a 2-factor in sparse graphs

We analyze the performance of a simple randomized algorithm for finding 2-factors in directed Hamiltonian graphs of out-degree at most two and in undirected Hamiltonian graphs of degree at most three. For the directed case, the algorithm finds a 2-factor in O ( n 2 ) expected time. The analysis of our algorithm is based on random walks on the line and interestingly resembles the analysis of a randomized algorithm for the 2-SAT problem given by Papadimitriou [On selecting a satisfying truth assignment, in: Proc. 32nd Annual IEEE Symp. on the Foundations of Computer Science (FOCS), 1991, p. 163]. For the undirected case, the algorithm finds a 2-factor in O ( n 3 ) expected time. We also analyze random versions of these graphs and show that cycles of length Ω ( n / log n ) can be found with high probability in polynomial time. This partially answers an open question of Broder et al. [Finding hidden Hamilton cycles, Random Structures Algorithms 5 (1994) 395] on finding hidden Hamiltonian cycles in sparse random graphs and improves on a result of Karger et al. [On approximating the longest path in a graph, Algorithmica 18 (1997) 82].

Tableaux for constructive concurrent dynamic logic

This is the first paper on constructive concurrent dynamic logic (CCDL). For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed by Pratt [V. Pratt, Semantical considerations on Floyd–Hoare logic, in: 17th Annual IEEE Symp. on Found. Comp. Sci., New York, 1976, pp. 109–121, V. Pratt, Applications of modal logic to programming, Studia Logica 39 (1980) 257–274] for nondeterministic sequential programs, and by Peleg [D. Peleg, Concurrent dynamic logic, Journal of the Association for Computing Machinery 34 (2) (1987), D. Peleg, Communication in concurrent dynamic logic, Journal of Computer and System Sciences 35 (1987)] for concurrent programs, for the purpose of proving properties of programs such as correctness. Here we define what it means for a dynamic logic formula to be forced to be true knowing only partial information about the results of assignments and tests. This informal CCDL semantics is formalized by intuitionistic Kripke frames modeling this partial information, and each such frame is interpreted as an idealized concurrent machine (a concurrent transition system). In CCDL, proofs and deductions are ω -height, ω -branching, well-founded labeled subtrees of ω ω . These are a generalization of the signed tableaux of Nerode [A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989, CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990, A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 (in press)] stemming from the prefix tableaux of Fitting [M.C. Fitting, Proof Methods for Modal and Intuitionistic Logic, Reidel, 1983]. We demonstrate the correctness of our tableau proofs, define consistency properties, prove that consistency properties yield models, construct systematic tableaux, prove that systematic tableaux yield a consistency property, and conclude that CCDL is complete. This infinitary semantics and proof procedure will be the primary guide for defining, in a sequel, the correct finitary CCDL (FCCDL) based on induction principles. FCCDL is suitable for implementation in constructive logic software systems such as Constable’s NUPRL or Huet-Coquand’s CONSTRUCTIONS. Our goal is to develop a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language, and for the extraction of concurrent programs from constructive proofs. Subsequent papers will introduce analogous logics for declarative and functional concurrent languages.

The Affine Hull of a Binary Automaton is Computable in Polynomial Time

We present the class of binary automaton, a new representation for the subsets of Nm that naturally extends the NDD ([Wolper, P. and B. Boigelot, An automata-theoretic approach to Presburger arithmetic constraints, in: Proc. 2nd Int. Symp. Static Analysis (SAS'95), Glasgow, UK, Sep. 1995, Lecture Notes in Computer Science 983 (1995), pp. 21–32], [Boudet, A. and H. Comon, Diophantine equations, Presburger arithmetic and finite automata, in: Proc. 21st Int. Coll. on Trees in Algebra and Programming (CAAP'96), Linköping, Sweden, Apr. 1996, Lecture Notes in Computer Science 1059 (1996), pp. 30–43]). We prove that the affine hull of the set of vectors represented by a binary automaton is computable in polynomial time. As application, we show that the set of place invariants [Ciardo, G., Petri nets with marking-dependent arc cardinality: Properties and analysis, in: Proc. 15th Int. Conf. Application and Theory of Petri Nets (ICATPN'94), Zaragoza, Spain, June 1994, Lecture Notes in Computer Science 815 (1994), pp. 179–198] of a counter system (an extension of the Broadcast Protocols [Emerson, E. A. and K. S. Namjoshi, On model checking for non-deterministic infinite-state systems, in: Proc. 13th IEEE Symp. Logic in Computer Science (LICS'98), Indianapolis, IN, USA, June 1998 (1998), pp. 70–80], [Delzanno, G., Verification of consistency protocols via infinite-state symbolic model checking: A case study, in: Proc. IFIP Joint Int. Conf. Formal Description Techniques & Protocol Specification, Testing, and Verification (FORTE-PSTV'00), Pisa, Italy, Oct. 2000, IFIP Conference Proceedings 183 (2000), pp. 171–186], [Delzanno, G., Constraint-based verification of parameterized cache coherence protocols, Formal Methods in System Design. To appear], the Reset/Transfer Petri Nets [Dufourd, C., A. Finkel and P. Schnoebelen, Reset nets between decidability and undecidability, in: Proc. 25th Int. Coll. Automata, Languages, and Programming (ICALP'98), Aalborg, Denmark, July 1998, Lecture Notes in Computer Science 1443 (1998), pp. 103–115], [Ciardo, G., Petri nets with marking-dependent arc cardinality: Properties and analysis, in: Proc. 15th Int. Conf. Application and Theory of Petri Nets (ICATPN'94), Zaragoza, Spain, June 1994, Lecture Notes in Computer Science 815 (1994), pp. 179–198] and the linear systems [Finkel, A. and J. Leroux, How to compose Presburger-accelerations: Applications to broadcast protocols, in: Proc. 22nd Conf. Found. of Software Technology and Theor. Comp. Sci. (FST&TCS'2002), Kanpur, India, Dec. 2002, Lecture Notes in Computer Science 2556 (2002), pp. 145–156]), is computable in polynomial time.

The correspondence between partial metrics and semivaluations

Partial metrics, or the equivalent weightable quasi-metrics, have been introduced in Matthews (Proc. 8th Summer Conf. on General Topology and Applications; Ann. New York Acad. Sci. 728 (1994) 183) as part of the study of the denotational semantics of data flow networks (Theoret. Comput. Sci. 151 (1995) 195). The interest in valuations in connection to Domain Theory derives from e.g. Jones and Plotkin (LICS ’89, IEEE Computer Society Press, Silver Spring, MD, 1998, pp. 186–195), Jones (Ph.D. Thesis, University of Edinburgh, 1989), Edalat (LICS’94, IEEE Computer Society Press, Silver Spring, MD, 1994) and Heckmann (Fund. Inform. 24(3) (1995) 259). Connections between partial metrics and valuations have been discussed in the literature, e.g. O'Neill (in: S. Andima et al. (Eds.), Proc. 11th Summer Conf. on General Topology and Applications; Ann. New York Acad. Sci. 806 (1997) 304), Bukatin and Scott (in: S. Adian, A. Nerode (Eds.), Logical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 1234, Springer, Berlin, 1997, pp. 33–43) and Bukatin and Shorina (in: M. Nivat (Ed.), Foundations of Software Science and Computation Structures, Lecture Notes in Computer Science, Vol. 1378, Springer, Berlin, 1998, pp. 125–139). In each case, partial metrics are generated from strictly increasing valuations. We analyze the precise relationship between these two notions. It is well known that characterizations of partial metrics in general are hard to obtain, as witnessed by the open characterization problems in the survey paper Nonsymmetric Topology (Kúnzi (Bolyai Soc. Math. Stud. 4 (1993) 303). Our approach to obtaining such a characterization involves the isolation of a “mathematically nice” class of spaces, which is sufficiently large to incorporate the quantitative domain theoretic examples involving partial metric spaces. For these purposes we focus on the class of quasi-metric semilattices. These structures, as will be illustrated, arise naturally in quantitative domain theory and include in particular the class of totally bounded Scott domains discussed in Smyth (in: G.M. Reed, A.W. Roscoe, R.F. Wachter (Ed.), Topology and Category Theory in Computer Science, Oxford University Press, Oxford, 1991, pp. 207–229), the Baire quasi-metric spaces of (Theoret. Comput. Sci. 151 (1995) 195), the complexity spaces of Schellekens (in: Proc. MFPS 11, Electronic Notes in Theoretical Computer Science, Vol. I, Elsevier, Amsterdam, 1995, pp. 211–232) and the interval domain (Proc. Twelfth Ann. IEEE Symp. on Logic in Computer Science, IEEE Press, New York, 1997, pp. 248–257). We introduce the notion of a semivaluation, which generalizes the fruitful notion of a valuation on a lattice to the context of semilattices and establish a correspondence between partial metric semilattices and semivaluation spaces.

Randomly coloring graphs with lower bounds on girth and maximum degree

AbstractWe consider the problem of generating a random q‐coloring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if the maximum degree Δ &gt; c1ln n and the girth g &gt; c2ln Δ (n = |V|) for sufficiently large c1, c2, then this chain mixes rapidly provided q/Δ &gt; β, where β ≈ 1.763 is the root of β = e1/β. For this class of graphs, this beats the 11Δ/6 bound of Vigoda E. Vigoda, Improved bounds for sampling colorings, Proc 40th Annu IEEE Symp Foundations of Computer Science, 1999, pp. 51–59 for general graphs. We extend the result to random graphs. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 167–179, 2003