A Note on Solving Problems of Substantially Super-linear Complexity in No(1) Rounds of the Congested Clique

Channel estimation based on Pilot Symbol Assisted Modulation (PSAM) has been investigated for OFDM systems on time-varying frequency-selective channels in different literature. The varying properties of the channel degrades the performance of the OFDM system which is perceived as special case of multi-carrier transmission. This paper investigates the performance of PSAM polynomial interpolation based channel estimation for OFDM systems on time-varying frequency-selective channels. The PSAM polynomial interpolation channel estimation is based on block type pilot arrangement. The SER performance of the OFDM system, and computational time complexities of the PSAM polynomial channel estimation are analysed for different fading rates, frame lengths and polynomial orders (P-orders). The SER performance is documented assuming 16-QAM as the modulation scheme in the OFDM system. From the computer simulation results, we summarize that the SER performance of polynomial based channel estimator is highly dependent on the SNR and the fading rate. Although, low P-orders exhibit good SER performance most significantly at low SNR. Also, the lower the P-orders the better SER performance and computational time complexity trade-off because high P-orders exhibit more computational delay and time complexity.

We study two fundamental graph problems, Graph Connectivity (GC) and Minimum Spanning Tree (MST), in the well-studied Congested Clique model, and present several new bounds on the time and message complexities of randomized algorithms for these problems. No non-trivial (i.e., super-constant) time lower bounds are known for either of the aforementioned problems; in particular, an important open question is whether or not constant-round algorithms exist for these problems. We make progress toward answering this question by presenting randomized Monte Carlo algorithms for both problems that run in O(log log log n) rounds (where n is the size of the clique). Our results improve by an exponential factor on the long-standing (deterministic) time bound of O(log log n) rounds for these problems due to Lotker et al. (SICOMP 2005). Our algorithms make use of several algorithmic tools including graph sketching, random sampling, and fast sorting.The second contribution of this paper is to present several almost-tight bounds on the message complexity of these problems. Specifically, we show that Ω(n2) messages are needed by any algorithm (including randomized Monte Carlo algorithms, and regardless of the number of rounds) that solves the GC (and hence also the MST) problem if each machine in the Congested Clique has initial knowledge only of itself (the so-called KT0 model). In contrast, if the machines have initial knowledge of their neighbors' IDs (the so-called KT1 model), we present a randomized Monte Carlo algorithm for MST that uses O(n polylog n) messages and runs in O(polylog n) rounds. To complement this, we also present a lower bound in the KT1 model that shows that Ω(n) messages are required by any algorithm that solves GC, regardless of the number of rounds used. Our results are a step toward understanding the power of randomization in the Congested Clique with respect to both time and message complexity.

The paper focuses on analysing the computational time complexity of Frontal Cellular Automata (FCAs) and comparing it with Classic Cellular Automata (CCAs). Some variants of CCAs and FCAs are described and presented by showing differences in their structure and transition rules. Several variants of simple two-dimensional (2D) CAs and four variants of three-dimensional (3D) CAs for grain growth have been developed, tested and analysed. These four 3D CA algorithms are described. The calculation time of several simulation cases is measured for 2D and 3D CAs. The computational time complexity is determined on the basis of these measurements. The paper also takes into account the parallelisation of calculations with CAs. Time measurements show the possibility of accelerating the calculations. The paper also presents examples of the application of FCAs to solidification, recrystallisation, phase transformation and grain refinement with giving their simulation time. The computational complexity of different CAs is discussed, and FCAs with cells organised into linked lists show the lowest computational complexity. The paper ends with conclusions highlighting the low computational complexity and time efficiency of FCA.

Linearization of nonlinear filter generators and its application to cryptanalysis of stream ciphers

Replacement sort revisited: The “gold standard” unearthed!

The 38th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC 2019) was held on July 29-August 2, 2019 at the Double Tree Hilton hotel in Toronto, Canada. With three keynotes, over 40 accepted papers, over 20 accepted brief announcements, two workshops, and roughly 150 attendants, PODC 2019 constituted a composition of fascinating improvements in many areas of distributed and parallel computing. On the evening of the 31st of July, the conference banquet was held on a cruise over beautiful Lake Ontario and included the best papers award ceremony. The best paper award went to Yi-Jun Chang, and Thatchaphol Saranurak for their work titled, \Improved Distributed Expander Decomposition and Nearly Optimal Triangle Enumeration" [19]; two best student paper awards were given to Yi-Jun Chang, Manuela Fischer, and Yufan Zheng for their work titled, \The Complexity of (Δ + 1) Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation" [17] which was co-authored with Mohsen Gha ari, and Jara Uitto, and to Michal Dory and Dean Leitersdorf for the work on \Fast Approximate Shortest Paths in the Congested Clique" [16] which was co-authored with Keren Censor-Hillel, and Janne H. Korhonen. Congratulations to all the awardees and a special congratulations to Yi-Jun Chang for having received both awards! This review would be incomplete without mentioning perhaps one of the most notable results in the eld in recent years which was uploaded to the online archive just days before the conference gathered, and which was not presented at PODC 2019 but a ected many works presented at the conference: the work titled, ¶olylogarithmic-Time Deterministic Network Decomposition and Distributed Derandomization" [48] by Vaclav Rozhon, and Mohsen Gha ari. Throughout the entire conference there was talk regarding the implications of this work, culminating with perhaps one of the more memorable moments of PODC 2019, where Mohsen described this result during his talk on a di erent paper which he co-authored with Fabian Kuhn - Mohsen quoted from his and Kuhn's paper [31]: \we provide results that are in some sense the strongest that one can achieve, barring a major breakthrough", and on the next slide was that major breakthrough - a picture of Vaclav Rozhon along with the rst page of [48]. Congratulations to the authors on this work! We hope that this review will give readers the opportunity to experience some of PODC 2019 and potentially attend the conference in future years. Thank you to the organizers and authors for a captivating and though-provoking conference!

In this paper, we present new randomized algorithms that improve the complexity of the classic (Δ+1)-coloring problem, and its generalization (Δ+1)-list-coloring, in three well-studied models of distributed, parallel, and centralized computation: Distributed Congested Clique: We present an O(1)-round randomized algorithm for (Δ + 1)-list-coloring in the congested clique model of distributed computing. This settles the asymptotic complexity of this problem. It moreover improves upon the O(log* Δ)-round randomized algorithms of Parter and Su [DISC'18] and O((log log Δ)⋅ log* Δ)-round randomized algorithm of Parter [ICALP'18].Massively Parallel Computation: We present a randomized (Δ + 1)-list-coloring algorithm with round complexity O(√ log log n ) in the Massively Parallel Computation (MPC) model with strongly sublinear memory per machine. This algorithm uses a memory of O(nα) per machine, for any desirable constant α > 0, and a total memory of O (m), where m is the number of edges in the graph. Notably, this is the first coloring algorithm with sublogarithmic round complexity, in the sublinear memory regime of MPC. For the quasilinear memory regime of MPC, an O(1)-round algorithm was given very recently by Assadi et al. [SODA'19].Centralized Local Computation: We show that (Δ + 1)-list-coloring can be solved by a randomized algorithm with query complexity Δ O(1) … O(log n), in the centralized local computation model. The previous state of the art for (Δ+1)-list-coloring in the centralized local computation model are based on simulation of known LOCAL algorithms. The deterministic O(√ Δ poly log Δ + log* n)-round LOCAL algorithm of Fraigniaud et al. [FOCS'16] can be implemented in the centralized local computation model with query complexity ΔO(√ Δ poly log Δ) … O(log* n); the randomized O(log* Δ) + 2^O(√ log log n)-round LOCAL algorithm of Chang et al. [STOC'18] can be implemented in the centralized local computation model with query complexity ΔO(log* Δ) … O(log n).

Input image pixels classification into two intensities like black and white as foreground and background respectively refers to image binarization. Binarization with a local threshold value is termed as adaptive image binarization. Locally adaptive thresholding techniques are local pixels dependent process. Local environment dependent process is normally time consuming one and hence its computational time complexity is also local region dependent. Adaptation depends on the local region contrast condition. Low contrast region may not be adapted correctly. This article presents a new locally adaptive fast binarization technique applied on contrast stretched domain of an input image. The local adaptation is based on the mean of the 9 local block boundary pixels. As it associates only 9 pixels for mean calculation, its computational time complexity is free from local reason block size. As it applies on contrast stretched domain image, it can adapt low contrast region for binarization while other techniques fail. Not only its low contrast adapting capability, it has a local block size free computational time complexity. Hence it is more convenient to adapt the low contrast region very fast as compared with other techniques. From the experimental results, it is observed that it yields fast better result than other related local techniques.

An Asymptotic Approach for Testing P0-Matrices

The notion that dissipation begets self-organization has remained informal, and not susceptible to rigorous proof or refutation, largely through lack of an adequate mathematical definition of organization. The chapter explores alternative definitions, proposes that organization be defined as logical depth, a notion based on algorithmic information and computational time complexity. Two rather different kinds of computing resources have been considered in the theory of computational complexity: static or definitional resources such as program size, and dynamic resources such as time and memory. Algorithmic information theory allows a static complexity or information content to be defined both for finite and for infinite objects, as the size in bits of the smallest program to computer the object on a standard universal computer. Finite strings, such as minimal programs, which are incompressible or nearly so are called algorithmically random.

Efficient solving of the group technology problem

The current development of Support Vector Machines (SVM) has reached a bottleneck, with issues such as long training times and weak interpretability when dealing with large-scale, multi-dimensional data. This paper introduces the concept of Quantum Support Vector Machines (QSVM) and achieves efficient solutions through quantum algorithms such as the HHL algorithm. The research designs a computational architecture that combines classical and quantum computing, utilizing the Pauli decomposition of Hermitian matrices to simulate the quantum simulation of Hamiltonian quantities and implementing the quantum simulation of unitary operators. Based on the conclusions, a complete quantum linear solver circuit is designed, achieving exponential growth in computational complexity. Experiments using the Iris dataset demonstrate the excellent classification performance of QSVM, which outperform classical SVM in classification accuracy, computational time complexity, and memory requirements. More efficient quantum mapping algorithms and quantum circuit optimization methods are implemented, providing new ideas and methods for the application of SVM to large-scale datasets.

Summary form only given. We present a probabilistic parameterized algorithm for the problem of vertex cover with time complexity O(p2/sup k/), where k is a parameter of the given instance, and p is a polynomial function on the input size. Furthermore, we implement this algorithm within sticker model by DNA computing, with space complexity O(2/sup k/) and polynomial time complexity O(n/sup 2/), where n is the number of vertexes.

In this letter, we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling all OFDM-IM waveforms maximizes the spectral efficiency (SE) gain over the classic OFDM but, as far as we know, the computational overhead of the resulting mapper remains conjectured as prohibitive across the OFDM-IM literature. We show that the largest number of binomial coefficient calculations performed by the original OFDM-IM mapper is polynomial on the number of subcarriers, even under the setup that maximizes the SE gain over OFDM. Also, such coefficients match the entries of the so-called Pascal's triangle (PT). Thus, by assisting the OFDM-IM mapper with a PT table, we show that the maximum SE gain over OFDM can be achieved under polynomial (rather than exponential) time and space complexities.

Computer science and physics have been closely linked since the birth of modern computing. This book is about that link. John von Neumann’s original design for digital computing in the 1940s was motivated by applications in ballistics and hydrodynamics, and his model still underlies today’s hardware architectures. Within several years of the invention of the first digital computers, the Monte Carlo method was developed, putting these devices to work simulating natural processes using the principles of statistical physics. It is difficult to imagine how computing might have evolved without the physical insights that nurtured it. It is impossible to imagine how physics would have evolved without computation. While digital computers quickly became indispensable, a true theoretical understanding of the efficiency of the computation process did not occur until twenty years later. In 1965, Hartmanis and Stearns [227] as well as Edmonds [139, 140] articulated the notion of computational complexity, categorizing algorithms according to how rapidly their time and space requirements grow with input size. The qualitative distinctions that computational complexity draws between algorithms form the foundation of theoretical computer science. Chief among these distinctions is that of polynomial versus exponential time. A combinatorial problem belongs in the complexity class P (polynomial time) if there exists an algorithm guaranteeing a solution in a computation time, or number of elementary steps of the algorithm, that grows at most polynomially with input size. Loosely speaking, such problems are considered computationally feasible. An example might be sorting a list of n numbers: even a particularly naive and inefficient algorithm for this will run in a number of steps that grows as O(n2), and so sorting is in the class P. A problem belongs in the complexity class NP (non-deterministic polynomial time) if it is merely possible to test, in polynomial time, whether a specific presumed solution is correct. Of course, P ⊆ NP: for any problem whose solution can be found in polynomial time, one can surely verify the validity of a presumed solution in polynomial time.