Review of Introduction to Distributed Algorithms

The papers in this volume were presented at the 43rd ACM Symposium on Theory of Computing (STOC), held June 6-8, 2011 in San Jose, California, as part of the fifth Federated Computing Research Conference (FCRC). STOC is sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT). The papers at STOC were selected by the program committee from among 304 submissions received by November 4, 2010 (5 of which were withdrawn by authors during the review process). The committee did its work by a combination of extensive electronic discussion and a physical meeting of the entire committee in San Francisco on January 26-27, 2011. These proceedings contain the 84 papers that were accepted to STOC, one of which is a merge of two related submissions. Three pairs of papers having similar results shared presentation slots at the conference, for a total of 81 talks. All submissions received careful consideration, but they were not refereed in a formal sense. Authors are encouraged to submit full versions of their papers to journals for a complete review and archival publication. The committee selected two papers for a Best Paper Award: "Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs," by Paul Christiano, Jonathan A. Kelner, Aleksander Madry, Daniel A. Spielman, and Shang-Hua Teng, and "Subexponential Lower Bounds for Randomized Pivoting Rules for the Simplex Algorithm," by Oliver Friedmann, Thomas Dueholm Hansen, and Uri Zwick. The committee selected "Analyzing Network Coding Gossip Made Easy" by Bernhard Haeupler for the Danny Lewin Best Student Paper Award. STOC was preceded by an FCRC plenary talk on June 5 given by Leslie Valiant as recipient of the 2011 ACM Turing Award for his transformative contributions to the theory of computation, including the theory of probably approximately correct (PAC) learning, the complexity of enumeration and of algebraic computation, and the theory of parallel and distributed computing. At the conference, the 11th Knuth Prize was awarded to Ravi Kannan for his work on algorithmic techniques that have fundamentally contributed to computational complexity, discrete mathematics, geometry, and operations research. He presented the Knuth Prize Lecture as an FCRC plenary talk on the morning of June 7. The program committee also decided to add a Poster Session, held on the evening of June 6, to increase the opportunities for disseminating and discussing research at the conference. Posters were not refereed; any registered FCRC attendee could present a poster on research in any aspect of theoretical computer science.

The papers in this volume were presented at the DIALM-POMC Joint Workshop on Foundations of Mobile Computing on October 1, 2004 in Philadelphia, Pennsylvania, USA. This workshop was held in conjunction with the ACM International Conference on Mobile Computing and Networking (MobiCom). DIALM-POMC was sponsored by the ACM Special Interest Group on Mobility of Systems, Users, Data, and Computing (SIGMOBILE) in cooperation with the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT).The Program Committee selected these thirteen papers from thirty-five submissions based on their perceived quality and originality and their relevance to the workshop theme. DIALM-POMC is devoted to discrete algorithms and discrete modeling in the context of mobile and wireless computing and communications. Efficient mobile computing and communication raise difficult algorithmic questions in areas such as frequency allocation, energy-efficient routing, algorithms for specific problems, data management in distributed sensor networks, and security. One workshop goal is to bring together practitioners and theoreticians in discrete and distributed algorithms for mobile applications.Because these papers are limited in size, many cannot contain full proofs of performance and/or full experimental results. Therefore, more complete and polished versions of these papers may appear later in archival journals. In particular, selected accepted papers from this workshop will appear in a special issue of Algorithmica.This workshop is the second merging of two workshops, DIAL-M (Discrete Algorithms and Methods for Mobile Computing and Communications), which was held annually in 1997-2002 as a workshop in conjunction with MobiCom; and POMC (Principles of Mobile Computing), which was held in 2001 in conjunction with the ACM Symposium on Principles of Distributed Computing (PODC), and in 2002 in conjunction with the International Symposium on Distributed Computing (DISC). The first joint DIALM-POMC meeting was held in conjunction with MobiCom in 2003.

The committee decided to award the 2019 Edsger W. Dijkstra Prize in Distributed Computing to Alessandro Panconesi and Aravind Srinivasan for their paper Randomized Distributed Edge Coloring via an Extension of the Chernoff-Hoeffding Bounds, SIAM Journal on Computing, volume 26, number 2, 1997, pages 350-368. A preliminary version of this paper appeared as Fast Randomized Algorithms for Distributed Edge Coloring, Proceedings of the Eleventh Annual ACM Symposium Principles of Distributed Computing (PODC), 1992, pages 251-262.The paper presents a simple synchronous algorithm in which processes at the nodes of an undirected network color its edges so that the edges adjacent to each node have different colors. It is randomized, using 1.6Δ + O(log1+ζn) colors and O(log n) rounds with high probability for any constant ζ>0, where n is the number of nodes and is the maximum degree of the nodes. This was the first nontrivial distributed algorithm for the edge coloring problem and has influenced a great deal of follow-up work. Edge coloring has applications to many other problems in distributed computing such as routing, scheduling, contention resolution, and resource allocation.In spite of its simplicity, the analysis of their edge coloring algorithm is highly nontrivial. Chernoff-Hoeffding bounds, which assume random variables to be independent, cannot be used. Instead, they develop upper bounds for sums of negatively correlated random variables, for example, which arise when sampling without replacement. More generally, they extend Chernoff-Hoeffding bounds to certain random variables they call λ-correlated. This has directly inspired more specialized concentration inequalities. The new techniques they introduced have also been applied to the analyses of important randomized algorithms in a variety of areas including optimization, machine learning, cryptography, streaming, quantum computing, and mechanism design.

Qualitative Problems in Matrix Theory

We give a new construction of pseudorandom generators from any one-way function. The construction achieves better parameters and is simpler than that given in the seminal work of H\aastad, Impagliazzo, Levin, and Luby [SIAM J. Comput., 28 (1999), pp. 1364--1396]. The key to our construction is a new notion of next-block pseudoentropy, which is inspired by the notion of “inaccessible entropy” recently introduced in [I. Haitner, O. Reingold, S. Vadhan, and H. Wee, Proceedings of the $41$st Annual ACM Symposium on Theory of Computing (STOC), 2009, pp. 611--620]. An additional advantage over previous constructions is that our pseudorandom generators are parallelizable and invoke the one-way function in a nonadaptive manner. Using [B. Applebaum, Y. Ishai, and E. Kushilevitz, SIAM J. Comput., 36 (2006), pp. 845--888], this implies the existence of pseudorandom generators in NC$^0$ based on the existence of one-way functions in NC$^1$.

We present a positive obfuscation result for a traditional cryptographic functionality. This positive result stands in contrast to well-known impossibility results (Barak et al. in Advances in Cryptology—CRYPTO’01, 2002), for general obfuscation and recent impossibility and implausibility (Goldwasser and Kalai in 46th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 553–562, 2005) results for obfuscation of many cryptographic functionalities.Whereas other positive obfuscation results in the standard model apply to very simple point functions (Canetti in Advances in Cryptology—CRYPTO’97, 1997; Wee in 37th ACM Symposium on Theory of Computing (STOC), pp. 523–532, 2005), our obfuscation result applies to the significantly more complex and widely-used re-encryption functionality. This functionality takes a ciphertext for message m encrypted under Alice’s public key and transforms it into a ciphertext for the same message m under Bob’s public key.To overcome impossibility results and to make our results meaningful for cryptographic functionalities, our scheme satisfies a definition of obfuscation which incorporates more security-aware provisions.

We study problems in randomized communication complexity when the protocol is only required to attain some small advantage over purely random guessing, i.e., it produces the correct output with probability at least $$\epsilon$$ greater than one over the codomain size of the function. Previously, Braverman and Moitra (in: Proceedings of the 45th symposium on theory of computing (STOC), ACM, pp 161–170, 2013) showed that the set-intersection function requires $$\Theta(\epsilon{n})$$ communication to achieve advantage $$\epsilon$$ . Building on this, we prove the same bound for several variants of set-intersection: (1) the classic “tribes” function obtained by composing with And (provided $$1/\epsilon$$ is at most the width of the And), and (2) the variant where the sets are uniquely intersecting and the goal is to determine partial information about (say, certain bits of the index of) the intersecting coordinate.

Previous article Next article Lower and Upper Bounds for the Number of Lattice Points in a SimplexAharon Gavriel Beged-dovAharon Gavriel Beged-dovhttps://doi.org/10.1137/0122012PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. G. Beged-Dov, Some computational aspects of the P printers M paper mills trim problem, Business Administration, 2 (1970), 15–34 Google Scholar[2] P. C. Gilmore and , R. E. Gomory, A linear programming approach to the cutting-stock problem, Operations Res., 9 (1961), 849–859 MR0137589 0096.35501 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Homotopy techniques for solving sparse column support determinantal polynomial systemsJournal of Complexity, Vol. 66 Cross Ref Percolating sets in bootstrap percolation on the Hamming graphs and triangular graphsEuropean Journal of Combinatorics, Vol. 92 Cross Ref Polynomial Approximation of Anisotropic Analytic Functions of Several Variables16 July 2020 | Constructive Approximation, Vol. 51 Cross Ref Greedy approximations by signed harmonic sums and the Thue–Morse sequenceAdvances in Mathematics, Vol. 366 Cross Ref Sampling inequalities for anisotropic tensor product grids8 January 2019 | IMA Journal of Numerical Analysis, Vol. 107 Cross Ref Novel results for the anisotropic sparse grid quadratureJournal of Complexity, Vol. 47 Cross Ref On tensor product approximation of analytic functionsJournal of Approximation Theory, Vol. 207 Cross Ref Hyperbolic cross approximation in infinite dimensionsJournal of Complexity, Vol. 33 Cross Ref Rethinking the encounter probability for direct-to-target nuclear attacks for aviation security5 May 2011 | Journal of Transportation Security, Vol. 4, No. 3 Cross Ref Эффективные оценки производных обратной функцииИзвестия Российской академии наук. Серия математическая, Vol. 72, No. 4 Cross Ref Improved lower and upper bounds for the number of feasible solutions to a knapsaek problemOptimization, Vol. 19, No. 6 Cross Ref APPLICATION OF OPERATIONS RESEARCH IN PAPER PROCUREMENT Cross Ref The Number of Feasible Solutions to a Knapsack ProblemO. Achou12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 27, No. 4AbstractPDF (209 KB)Bounds on the Number of Feasible Solutions to a Knapsack ProblemThomas A. Lambe12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 26, No. 2AbstractPDF (229 KB)The Paper Trim Problem: A Variable Demand AnalysisA I I E Transactions, Vol. 6, No. 1 Cross Ref A Remark on “an Inequality for the Number of Lattice Points in a Simplex”Manfred W. Padberg12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 20, No. 4AbstractPDF (253 KB) Volume 22, Issue 1| 1972SIAM Journal on Applied Mathematics History Submitted:09 December 1969Published online:12 July 2006 InformationCopyright © 1972 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0122012Article page range:pp. 106-108ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Scheduling multicasts on unit-capacity trees and meshes

In "A linear-time algorithm for triangulating a simple polygon" [Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing (1986), 380-388. 486], the analysis showing that the authors' triangulation algorithm runs in linear time is incorrect, and indeed the algorithm does not run in linear time in the worst case. So far they have been unable to obtain a linear-time algorithm for the triangulation problem. They have been able to obtain an O(n loglogn)-time algorithm, however. The details are described in "An O(n loglogn)-Time Algorithm for Triangulating a Simple Polygon," SIAM Journal on Computing 17, 1 (February, 1988), to appear.

It is my pleasure to welcome you to the 10th Onward!. This year marks its first year as a bona fide SIGPLAN symposium; its proper name is ACM Symposium on New Ideas in Programming and Reflections on Software. Its familiar name, though, remains Onward!---with the exclamation point. "New ideas in programming" means that we are interested in ideas that can move us forward or radically sideways. A good Onward! paper has two characteristics: readers will wish they had thought of it, and they will believe "it might just work." We don't expect detailed proof the idea will work, but we don't accept pure claims. Onward! papers are well written, well argued, and compelling. They are generally bigger than technical papers, more radical, more visionary, wider ranging, more thought provoking, more frustrating even. Here is what they are not: ordinary OOPSLA papers with lousy validation. "Reflections on software" means that sometimes the way forward begins by looking back and thinking hard, finding new (and better) ways to view what has gone before, in order to provide a new vector. We call such papers "essays." Essays are reflective, often personal, and cover a lot of ground in unexpected ways. Essays are hard to write. Very hard to write. Over the years we have had a good number submitted, but only a scarce few accepted. Here is what they are not: ordinary OOPSLA papers with lousy validation. We welcome submissions about every and any aspect of programming, software, and software engineering. When what you want to say doesn't fit into the research papers or essays bucket, you can submit a film. This year we accepted seven out of 23 research papers and five films for presentation and publications. While authors of research papers are proficient at writing technical papers, the essay form has proven to be more difficult, and this year, though we had 13 submissions, none were taken. We decided, then, that this year's essays track take the form of a writers' workshop in which a couple of good essayists will coach budding writers in the essay form. Our keynote speaker is Markus Püschel who is well known for his work on Spiral, an automatic performance programming framework for a small, but important class of functions called linear transforms. In his talk he will draw attention to the performance / productivity problem for mathematical applications and make the case for a more interdisciplinary attack.

Fast deterministic consensus in a noisy environment

It is our pleasure to welcome you to the 41st ACM Symposium on Principles of Distributed Computing (PODC 2022). Following two years of pandemic-related virtual meetings, PODC 2022 is planned as an in-person event, taking place July 25-29 in Salerno, Italy. PODC is one of the premier international forums on the theory, design, analysis, implementation and application of distributed systems and networks. It spans all areas of distributed computing and aims at improving the understanding of the principles underlying distributed computing. The annual symposium is sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) and the ACM Special Interest Group in Operating Systems (SIGOPS). These proceedings contain 40 regular papers and 19 brief announcements, which will be presented at the conference. They also include the abstracts of three invited keynote lectures by Seny Kamara (Brown University), Merav Parter (Weizmann Institute of Science), and Michael L. Scott (University of Rochester). Furthermore, they contain the citations for two awards jointly sponsored by PODC and the EATCS Symposium on Distributed Computing (DISC): the Edsger W. Dijkstra Prize in Distributed Computing, and the Principles of Distributed Computing Doctoral Dissertation Award. PODC 2022 received 145 submissions, of which 134 were submitted as regular papers and 11 as brief announcements. With the help of approximately 150 external reviewers, the program committee selected 40 papers for regular presentation and 19 brief announcements, some of which had been submitted as regular papers. A lightweight double-blind reviewing process was employed, ensuring that submissions did not reveal the identity of the authors. Each submission was evaluated by at least three reviewers. The reviewing process comprised two rounds, with approximately half of the submissions making the first-round cut. Final decisions were made in a virtual program committee meeting spanning two days.

Computability is one of the fundamental notions of mathematics and computer science, trying to capture the effective content of mathematics and its applications. Computability Theory explores the frontiers and limits of effectiveness and algorithmic methods. It has its origins in Godel's Incompleteness Theorems and the formalization of computability by Turing and others, which later led to the emergence of computer science as we know it today. Computability Theory is strongly connected to other areas of mathematics and theoretical computer science. The core of this theory is the analysis of relative computability and the induced degrees of unsolvability; its applications are mainly to Kolmogorov complexity and randomness as well as mathematical logic, analysis and algebra. Current research in computability theory stresses these applications and focuses on algorithmic randomness, computable analysis, computable model theory, and reverse mathematics (proof theory). Recent advances in these research directions have revealed some deep interactions not only among these areas but also with the core parts of computability theory. The goal of this Dagstuhl Seminar is to bring together researchers from all parts of computability theory and related areas in order to discuss advances in the individual areas and the interactions among those.

The transactional approach to contention management guarantees consistency by making sure that whenever two transactions have a conflict on a resource, only one of them proceeds. A major challenge in implementing this approach lies in guaranteeing progress, since transactions are often restarted. Inspired by the paradigm of non-clairvoyant job scheduling, we analyze the performance of a contention manager by comparison with an optimal, clairvoyant contention manager that knows the list of resource accesses that will be performed by each transaction, as well as its release time and duration. The realistic, non-clairvoyant contention manager is evaluated by the competitive ratio between the last completion time (makespan) it provides and the makespan provided by an optimal contention manager. Assuming that the amount of exclusive accesses to the resources is non-negligible, we present a simple proof that every work conserving contention manager guaranteeing the pending commit property achieves an O(s) competitive ratio, where s is the number of resources. This bound holds for the Greedy contention manager studied by Guerraoui et al. (Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 258–264, 2005) and is a significant improvement over the O(s 2) bound they prove for the competitive ratio of Greedy. We show that this bound is tight for any deterministic contention manager, and under certain assumptions about the transactions, also for randomized contention managers. When transactions may fail, we show that a simple adaptation of Greedy has a competitive ratio of at most O(ks), assuming that a transaction may fail at most k times. If a transaction can modify its resource requirements when re-invoked, then any deterministic algorithm has a competitive ratio Ω(ks). For the case of unit length jobs, we give (almost) matching lower and upper bounds.