Hardness Proofs Research Articles

XNLP-Completeness for Parameterized Problems on Graphs with a Linear Structure

AbstractIn this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing W[1]-hardness proofs for these problems, since XNLP-hardness implies W[t]-hardness for all t. It also indicates, via a conjecture by Pilipczuk and Wrochna (ACM Trans Comput Theory 9:1–36, 2018), that any XP algorithm for such problems is likely to require XP space. In particular, we show XNLP-completeness for natural problems parameterized by pathwidth, linear clique-width, and linear mim-width. The problems we consider are Independent Set, Dominating Set, Odd Cycle Transversal, (q-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set, Capacitated (Red-Blue) Dominating Set, Capacitated Vertex Cover and Bipartite Bandwidth.

Changing Your Love of Music by Stimulating the Brain

For many of us, listening to our favorite songs makes us feel happy, energetic, and inspired. One goal of brain research is to understand the role of the brain as we listen to music. For years, researchers have hypothesized that the brain areas involved in processing the music we hear are involved in musical pleasure—but they had no hard proof. By stimulating people’s brains using strong magnets, along with a brain-imaging technique that could see which areas of the brain were active, scientists have unraveled why we feel so awesome when we listen to our favorite jams. Now there is good evidence to show that our favorite tunes involve connections between specific brain areas, including the brain’s “reward center”—an area that makes us feel good when we do something that we like. These brain circuits provide a solid piece to this complex puzzle of why music makes us feel so good.

Algebraic Global Gadgetry for Surjective Constraint Satisfaction

The constraint satisfaction problem (CSP) on a finite relationalstructure B is to decide, given a set of constraints on variableswhere the relations come from B, whether or not there is an assignmentto the variables satisfying all of the constraints; the surjectiveCSP is the variant where one decides the existence of a surjective satisfyingassignment onto the universe of B. We present an algebraicframework for proving hardness results on surjective CSPs; essentially,this framework computes global gadgetry that permits one to presenta reduction from a classical CSP to a surjective CSP. We show how toderive a number of hardness results for surjective CSP in this framework,including the hardness of the disconnected cut problem, of theno-rainbow three-coloring problem, and of the surjective CSP on alltwo-element structures known to be intractable (in this setting). Ourframework thus allows us to unify these hardness results and revealcommon structure among them; we believe that our hardness proof forthe disconnected cut problem is more succinct than the original. Inour view, the framework also makes very transparent a way in whichclassical CSPs can be reduced to surjective CSPs.

PPAD-complete approximate pure Nash equilibria in Lipschitz games

Lipschitz games, in which there is a limit λ (the Lipschitz value of the game) on how much a player's payoffs may change when some other player deviates, were introduced about 10 years ago by Azrieli and Shmaya. They showed via the probabilistic method that n-player Lipschitz games with m strategies per player have ϵ-approximate pure Nash equilibria, for ϵ≥λ8nlog⁡(2mn). Here we provide the first hardness result for the corresponding computational problem, showing that even for a simple class of Lipschitz games (Lipschitz polymatrix games), finding ϵ-approximate pure equilibria is PPAD-complete, for suitable pairs of values ϵ(n), λ(n). Novel features of this result include both the proof of PPAD hardness (in which we apply a population game reduction from unrestricted polymatrix games) and the proof of containment in PPAD (by derandomizing the selection of a pure equilibrium from a mixed one). In fact, our approach implies containment in PPAD for any class of Lipschitz games where payoffs from mixed-strategy profiles can be deterministically computed. When instead considering games where only payoffs from action profiles can be deterministically computed, we provide two equivalent definitions of “randomized PPAD” and show that the generalized problem belongs to this class.

Pengembangan dan Pengelolaan Adat Budaya Melalui Pembentukan Rancangan Peraturan Desa Dongko, Kabupaten Trenggalek

The Trenggalek Regency is home to Dongko Village, which is found in the Dongko District. Dongko Village is one of the potential Tourism Villages because of the rich variety of its traditions and histories. Dongko's cultural customs are an integral part of the village's identity and must be safeguarded in both their physical and legal manifestations if the village is to continue to grow and be managed effectively. Empirical study was conducted, which depicts an investigative process present in all areas of social life, including volunteer work. The term "empirical research" refers to a kind of study in which hard data and proof are gathered by direct observation and experimentation. The author conducted the study by making personal observations in the wild. Due to a lack of specificity in Law 12 of 2011, the provisions of Law 6 of 2014 pertaining to villages are consulted in order to determine how to construct Village Regulations. The Village Regulation is a cornerstone of village life, as it governs the day-to-day operations of the village government and the community at large. In line with article 24 of Law No. 6 of 2014, the Perdes product stands as a symbol of the spread of democracy to the grassroots level. As a result, the PKM (Community Service) Team in Dongko Village, Dongko District, Trenggalek Regency uses the Legislation work program with one of its legal products, namely the drafting of Village Regulations, to restore the Village Regulations in accordance with the needs of the village communities.

On First Looking into Milton’s Shakespeare

ABSTRACT For Miltonists and early modern scholars in general, the identification of Milton’s copy of Shakespeare’s First Folio through the combined work of Claire Bourne and Jason Scott-Warren was exhilarating. At last there seemed hard proof of a bridge between the writers whom Samuel Taylor Coleridge described as the “twin peaks” of English literature. But what do Milton’s marginal brackets and editorial emendations tell us? This article addresses some of the patterns that can be found in the folio and considers how they might be connected to major concerns in Milton’s poetry, particularly through his reading of Romeo and Juliet.

Multistage s–t Path: Confronting Similarity with Dissimilarity

Addressing a quest by Gupta et al. (in: Proceedings of the 41st international colloquium on automata, languages, and programming (ICALP 2014), vol 8572 of LNCS. Springer, pp 563–575, 2014), we provide a first, comprehensive study of finding a short s–t path in the multistage graph model, referred to as the Multistages–tPath problem. Herein, given a sequence of graphs over the same vertex set but changing edge sets, the task is to find short s–t paths in each graph (“snapshot”) such that in the found path sequence the consecutive s–t paths are “similar”. We measure similarity by the size of the symmetric difference of either the vertex set (vertex-similarity) or the edge set (edge-similarity) of any two consecutive paths. We prove that these two variants of Multistages–tPath are already {text {NP}}-hard for an input sequence of only two snapshots and maximum vertex degree four. Motivated by this fact and natural applications of this scenario e.g. in traffic route planning, we perform a parameterized complexity analysis. Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness ({text {W[1]}}-hardness) regarding the parameter path length (solution size). As a further conceptual investigation, we then modify the multistage model by asking for dissimilar consecutive paths. As one of the main technical results (employing so-called representative sets known from non-temporal settings), we prove that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting with our W[1]-hardness proof of the corresponding similarity case. We also provide partially positive results concerning efficient and effective data reduction (kernelization).

Tight Bounds on the Convergence of Noisy Random Circuits to the Uniform Distribution

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.

The Complexity of Bipartite Gaussian Boson Sampling

Gaussian boson sampling is a model of photonic quantum computing that has attracted attention as a platform for building quantum devices capable of performing tasks that are out of reach for classical devices. There is therefore significant interest, from the perspective of computational complexity theory, in solidifying the mathematical foundation for the hardness of simulating these devices. We show that, under the standard Anti-Concentration and Permanent-of-Gaussians conjectures, there is no efficient classical algorithm to sample from ideal Gaussian boson sampling distributions (even approximately) unless the polynomial hierarchy collapses. The hardness proof holds in the regime where the number of modes scales quadratically with the number of photons, a setting in which hardness was widely believed to hold but that nevertheless had no definitive proof. Crucial to the proof is a new method for programming a Gaussian boson sampling device so that the output probabilities are proportional to the permanents of submatrices of an arbitrary matrix. This technique is a generalization of Scattershot BosonSampling that we call BipartiteGBS. We also make progress towards the goal of proving hardness in the regime where there are fewer than quadratically more modes than photons (i.e., the high-collision regime) by showing that the ability to approximate permanents of matrices with repeated rows/columns confers the ability to approximate permanents of matrices with no repetitions. The reduction suffices to prove that GBS is hard in the constant-collision regime.

Lifetime-Maximized Strong Barrier Coverage of 3D Camera Sensor Networks

Camera sensor networks (CSNs) have advantages on providing the precise and multimedia information for plenty of applications. The high coverage quality of CSNs especially satisfies the monitoring requirements of barrier coverage. In three-dimensional (3D) application scenarios, the tracking of the potential intruder in the monitored irregular spaces brings more difficulties and challenges on strong barrier coverage for CSNs. In this paper, we consider the strong barrier coverage problem in 3D CSNs and focus on the objective of monitoring the intruder with high resolution and maximizing the network lifetime. We firstly introduce the definition and hardness proof for the problem based on the irregular space model and the network model, which adopts the Region of Interest (ROI) sensing model with high effective resolution. Secondly, we design two sleep-and-awake scheduling algorithms for the problem in homogeneous and heterogeneous networks, respectively, which are based on the auxiliary graph transformation and the disjoint flows construction. To evaluate these algorithms’ performance on the lifetime maximization, we conduct extensive simulation experiments and analyze their results on their advantages and applicable scenarios.

On the rectangular knapsack problem

A recent paper by Schulze et al. (Math Methods Oper Res 92(1):107–132, 2020) presented the Rectangular Knapsack Problem (Rkp) as a crucial subproblem in the study on the Cardinality-constrained Bi-objective Knapsack Problem (Cbkp). To this end, they started an investigation into its complexity and approximability. The key results are an NP -hardness proof for a more general scenario than Rkp, and a 4.5-approximation for Rkp, raising the question of improvements for either result. In this note we settle both questions conclusively: we show that (a) Rkp is indeed NP -hard in the considered setting (and even in more restricted settings), and (b) there exists both a pseudopolynomial algorithm and a fully-polynomial time approximation scheme (i.e., efficient approximability within any desired ratio alpha >1) for Rkp.

Status and distribution of dormice (Mammalia, Gliridae) in Bulgaria

Here we summarize all available data about dormice (Gliridae) in Bulgaria, published one and our own observations, collected in the last 20 years. Four species are found in Bulgaria - the Forest Dormouse (Dryomys nitedula), the Edible Dormouse (Glis glis), the Hazel Dormouse (Muscardinus avellanarius) and the Roach’s Mouse-tailed Dormouse (Myomimus roachi). Altogether we collected 1200 records from 283 locations. A database has been created in which every single record is kept. The most common and widespread species are the Edible (G. glis) and Forest Dormouse (D. nitedula), found in 212 and 139 locations respectively. They inhabit mainly the deciduous and mixed forest in the country. The Hazel Dormouse (M. avellanarius) is found in 77 locations, the bulk of them are in the mountains, but there are some locations along the Danube and southeast Bulgaria. It prefers woods with a well-developed understorey. The Roach’s mouse-tailed dormouse (M. roachi) is the rarest one - found in 26 locations in southeast Bulgaria. In contrast to the other dormice, it avoids woods and lives in semi-open habitats with shrubs, tree lines, and islands in grasslands and agricultural fields. There are several anecdotal reports of the Garden Dormouse (Eliomys quercinus) but no hard proof exists for the presence of this species. We discussed the patterns of distribution, conservation status, and coexistence of Bulgarian dormice.

SHĪʿĪ READINGS OF HUMAN EVOLUTION: ṬABĀṬABĀʾĪ TO ḤAYDARĪ

AbstractWithin the context of Islamic discourse about evolution, this is the first study that focuses exclusively on the views of Kamāl al‐Ḥaydarī (b. 1957), a prominent Shīʿī thinker of the contemporary period. Ḥaydarī develops his views from Muḥammad Ḥusayn al‐Ṭabāṭabāʾī (1904–1981), the author of the seminal exegesis The Balance in Interpreting the Qurʾān (Al‐Mīzān fī Tafsīr al‐Qurʾān). Ṭabāṭabāʾī is very hesitant about accepting whether the Qurʾān can be read to indicate evolution and ultimately refuses it because of a lack of scientific evidence in his eyes. However, Ḥaydarī challenges the hesitation in Ṭabāṭabāʾī’s hermeneutics while nonetheless agreeing with him on the lack of hard scientific proof for macroevolution. Instead, Ḥaydarī proposes a novel, theological reading of evolution understood in a nonscientific sense. The article examines Ḥaydarī’s views on evolution, his creationist conclusions, his suggestion of multiple “Adams” in human and Prophetic origins, and his attempt to link evolution of consciousness with the Shīʿī belief in the Parousia of the Mahdī. His unique reading of scripture marks him as being radically different to any of the currently available opinions in the discourse of Islam and evolution.

Target Set Selection in Dense Graph Classes

In this paper, we study the Target Set Selection problem from a parameterized complexity perspective. Here for a given graph and a threshold for each vertex, the task is to find a set of vertices (called a target set) that activates the whole graph during the following iterative process. A vertex outside the active set becomes active if the number of so far activated vertices in its neighborhood is at least its threshold. We give two parameterized algorithms for a special case where each vertex has the threshold set to half of its neighbors (the so-called Majority Target Set Selection problem) for parameterizations by the neighborhood diversity and the twin cover number of the input graph. We complement these results from the negative side. We give a hardness proof for the Majority Target Set Selection problem when parameterized by (a restriction of) the modular-width---a natural generalization of both previous structural parameters. We also show the Target Set Selection problem parameterized by the neighborhood diversity or by the twin cover number is \sf W[1]-hard when there is no restriction on the thresholds.

Microtextured die using silicon stencil mask for micro-machining of stainless steel

Taking advantage that silicon (Si) can be processed realizing the fine structure with a high-aspect-ratio, a through-hole structure is applied as the hard mask for Ar+ ion-based dry etching of metal materials. Conventionally, the micro texturing of metal materials has the problem of the lack of the appropriate mask, which should be hard and high-temperature proof enabling the fine pattern. Si hard mask with about 2 μm wide through-hole structures is fabricated and used for realizing the fine and deep structure on the die material (SKD11 of the standard alloy tool steel). The aspect ratio of the trench obtained is about 2, confirming the effectiveness of the Si hard mask. The die is applied for pressing SUS304 steel transferring the microstructure. The realized embossed structure has an aspect ratio larger than 1.

Complexity of Scorpion Solitaire and applications to Klondike

Scorpion is a puzzle game that falls under the category of Solitaires. The problem of determining whether a starting configuration of a Solitaire game (generalized to contain an arbitrary number of cards) can lead to a winning configuration has been studied from the perspective of Computational Complexity for some of the most popular Solitaires, namely Free Cell [1], Klondike [2] and Spider [3], all resulting in hardness proofs. Scorpion, though, has a unique twist compared to the aforementioned ones: each card can be moved to cover only one other card. This property narrows the set of possible moves and makes a worthwhile issue investigating whether the same problem proved NP-complete for Free Cell, Klondike and Spider falls in P as far as Scorpion is considered. In this paper we prove that the problem of deciding whether an n-card s-suits initial configuration of Scorpion allows for a winning sequence of moves is NP-complete for any s≥1, and it remains so also when the initial configuration contains no face down (locked) cards and under a constant ratio constraint between deck size and tableau size. As a side effect of our results, we have also succeeded in negatively answering a question posed in [2], in that we prove that it is NP-complete to decide whether an n-card one red suit-one black suit configuration of the Klondike Solitaire allows for a winning sequence of moves.

The Complexity of Object Association in Multiple Object Tracking

Object association, i.e., the identification of which observations correspond to the same object, is a central task for the area of multiple object tracking. Two prominent models capturing this task have been introduced in the literature: the Lifted Multicut model and the more recent Lifted Paths model. Here, we carry out a detailed complexity-theoretic study of the problems arising from these two models that is aimed at complementing previous empirical work on object association. We obtain a comprehensive complexity map for both models that takes into account natural restrictions to instances such as possible bounds on the number of frames, number of tracked objects and branching degree, as well as less explicit structural restrictions such as having bounded treewidth. Our results include new fixed-parameter and XP algorithms for the problems as well as hardness proofs which altogether indicate that the Lifted Paths problem exhibits a more favorable complexity behavior than Lifted Multicut.

Hard core proof of the polyvinyl alcohol as a reducer for the formation of gold nanoparticles

In this paper, we report the direct synthesis of water dispersed gold nanoparticles encapsulated in polyvinyl alcohol (PVA), which acting as reducer to gold ion to gold metal and capping agent. The syntheses of the gold nanoparticles were carried with the direct addition of the aqueous HAuCl4 solution to aqueous PVA solution at 50 °C. Initially, the PVA solution was prepared by using 2 g of PVA per 100 ml of distilled water in a round bottom flask which was placed in oil bath placed over the magnetic stirrer. Subsequently, the aqueous solution HAuCl4 was added drop-wise to the PVA solution. Afterward, the solution was made viscous by heating at same temperature and casted in form of nanocomposites films. Various compositions of HAuCl4 (0.2 wt%, 0.5 wt%, 1.0 wt% and 1.5 wt%) with respect to PVA (films of Au-PVA nanocomposites) were prepared. Upon drying in ambient condition these films were analyzed with XRD, SEM, EDX, TGA, UV–Visible, and IR techniques. The XRD analysis reveals the fcc crystal structure with crystallite size nearly 22 nm. The crystallite size is in agreement with that obtained by SEM analysis which is in range of 25–30 nm and particles are nearly spherical in shape. Furthermore, the UV–visible analysis showed the surface plasmon resonance (SPR) band at ~ 550 nm which confirmed the formation of gold nanoparticles. It is further supported by the EDX analysis that showed the gold peaks in the spectrum.

Acyclic orders, partition schemes and CSPs: Unified hardness proofs and improved algorithms

Many computational problems arising in, for instance, artificial intelligence can be realized as infinite-domain constraint satisfaction problems (CSPs) based on partition schemes: a set of pairwise disjoint binary relations (containing the equality relation) whose union spans the underlying domain and which is closed under converse. We first consider partition schemes that contain an acyclic order and where the constraint language contains all unions of the basic relations; such CSPs are frequently occurring in e.g. temporal and spatial reasoning. We identify properties of such orders which, when combined, are sufficient to establish NP-hardness of the CSP and strong lower bounds under the exponential-time hypothesis, even for degree-bounded problems. This result explains, in a uniform way, many existing hardness results from the literature, and shows that it is impossible to obtain subexponential time algorithms unless the exponential-time hypothesis fails. However, some of these problems (including several important temporal problems), despite likely not being solvable in subexponential time, admit non-trivial improved exponential-time algorithm, and we present a novel improved algorithm for RCC-8 and related formalisms.

A simple proof of QBF hardness

We provide a simple and direct proof of the exponential hardness of the KBKF formulas in the proof system Q-Resolution.