Showing papers in "Sigact News in 2005"

Algorithmic problems in power management

Abstract: We survey recent research that has appeared in the theoretical computer science literature on algorithmic problems related to power management. We will try to highlight some open problem that we feel are interesting. This survey places more concentration on lines of research of the authors: managing power using the techniques of speed scaling and power-down which are also currently the dominant techniques in practice.

Guest Column: NP-complete problems and physical reality

Abstract: Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and "anthropic computing." The section on soap bubbles even includes some "experimental" results. While I do not believe that any of the proposals will let us solve NP-complete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics.

NP-complete Problems and Physical Reality

Abstract: Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing.” The section on soap bubbles even includes some “experimental” results. While I do not believe that any of the proposals will let us solve NP-complete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics.

SIGACT news online algorithms column 8

Abstract: Pros and cons of the competitive analysis have been discussed in the literature by many authors. Continuing this discussion in this quarter s column, Reza Dorrigiv and Alejandro Lopez-Ortiz review and compare various performance measures for online algorithms, highlighting their differences with respect to the competitive ratio. Many thanks to Reza and Alejandro for contributing this article.

A short introduction to failure detectors for asynchronous distributed systems

Abstract: Since the first version of Chandra and Toueg's seminal paper titled "Unreliable failure detectors for reliable distributed systems" in 1991, the failure detector concept has been extensively studied and investigated. This is not at all surprising as failure detection is pervasive in the design, the analysis and the implementation of a lot of fault-tolerant distributed algorithms that constitute the core of distributed system middleware.The literature on this topic is mostly technical and appears mainly in theoretically inclined journals and conferences. The aim of this paper is to offer an introductory survey to the failure detector concept for readers who are not familiar with it and want to quickly understand its aim, its basic principles, its power and limitations. To attain this goal, the paper first describes the motivations that underlie the concept, and then surveys several distributed computing problems showing how they can be solved with the help of an appropriate failure detector. So, this short paper presents motivations, concepts, problems, definitions, and algorithms. It does not contain proofs. It is aimed at people who want to understand basics of failure detectors.

Four colors suffice

Abstract: This column is a review of the recent book "Four colors suffice" by Robin Wilson (used copies available on Amazon for $11.50) that might interest the readers of this column since its almost three decades since the result was proven by Appel and Haken.

Guest column: inapproximability results via Long Code based PCPs

Abstract: Summer has come again. And what better way is there to spend a summer than to relax on a sandy beach, on a mountain top, or at a park's picnic tables, and... think theory! Summer is a particularly good time to attack the big questions whose openness just plain annoys you. In light of Reingold's L = SL result, does L-vs.-RL tempt you? If so, take it on! (But perhaps peek first at Reingold--Trevisan--Vadhan's ECCC TR05-022.) Are you convinced that UP = NP should imply the collapse of the polynomial hierarchy? Make it so! (But if you hope to do so via showing that UP is contained in the low hierarchy, peek first at Long--Sheu's 1996 MST article.) You know that S2 ⊆ SNP∩coNP2 ⊆ ZPPNP and SNP2 ⊆ ZPPNPNP, but believe that some of those "⊆"s are "=" s or are (gasp!) provably strict containments (thus giving some insight into whether recent improvements (Cai in FOCS 2001; Cai et al. in Information and Computation 2005) in the collapses of the polynomial hierarchy from assumptions that NP is in P/poly, (NP ∩ coNP)/poly, or coNP/poly are strict improvements)? Well, prove an "=" or find evidence for a strict containment... or to really make this a summer for us all to remember, prove a strict containment! Wishing you happy theorems.This article gives an overview of recent PCP constructions based on the Long Code and the inapproximability results implied by these constructions. We cover the inapproximability results for (1) MAX-3SAT and CLIQUE (2) Results for SPARSEST CUT, VERTEX COVER and MAX-CUT implied by the Unique Games Conjecture and (3) HYPERGRAPH VERTEX COVER and coloring problems on hypergraphs. The article aims at explaining the general framework that, loosely speaking, incorporates all the above results.

SIGACT news complexity theory column 48

Abstract: Here is a real gift to the field from David Johnson: After a thirteen year intermission, David is restarting his NP-completeness column. His column will now appear about twice yearly in ACM Transactions on Algorithms. Welcome back David, and thanks! And for those for whom a diet of two per year wont do, meals past can be found at http://www.research.att.com/~dsj/columns.html.

Review of "Computational Line Geometry, by H. Pottmann and J. Wallner", Springer Verlag, 2001

Abstract: How does the configuration of hinges of the limbs of a robot impact its motion? How can I describe visible phenomena from optics and mechanics? Will my packaging machine jam or create unattractive creases? How can I reconstruct objects that are mathematically simple to manipulate from scanned data? All these are rather applied questions and all these questions have to do with geometry. Some of these problems are new. They came about because of advances in mechanical engineering and data acquisition. Others are very old problems, like the attempts to explain focal lines created by lenses. Computers have in many ways altered how we can ask questions and find answers about such problems. While in the past \tracing curves" was a skill to acquire, this has become a task relegated to computer graphics. Instead we may want to worry about computational structures and algorithmic complexities of the algorithms to do this. We do have a vast literature on numerical methods of geometric objects based on splicing our objects into discrete meshes and treating discrete mesh points. This immediately gives the data structures and it allows us to ask questions of efficiency and accuracy. This body of knowledge typically deals with objects in Euclidean space with Cartesian coordinated and discrete approximations of differential operators on these objects. Literature on visualization and numerical methods in computer graphics usually follow this approach. Another approach is concerned with the computation of discrete and combinatorial structures in relationship to some geometrical situation. These structures again lend themselves to complexity analysis. How can a space best be partitioned? How can we find points of collisions efficiently? This is what many of us would understand to be \Computational Geometry". As with most classifications there is some overlap.

Review of "Graphs, Networks, and Algorithms (second edition) by Dieter Jungnickel", Springer-Verlag 2005

Abstract: Hollow filaments having longitudinal grooves and ridges that are readily split along the grooves and are especially adapted for use in a flocking process to form flocked products with a surface similar to suede. The hollow filaments have a denier of about 0.8 to about 3.35 and have a void area of 15 to 30% of the total area of the cross section of the fiber.

The Church-Turing thesis and its look-alikes

Abstract: "A function is mechanically computable (that is: computable by means of a machine) if and only if it is Turing-computable."

On quantum versions of record-breaking algorithms for SAT

Abstract: It is well known that a straightforward application of Grover's quantum search algorithm enables to solve SAT in O(2n/2) steps. Ambainis (SIGACT News, 2004) observed that it is possible to use Grover's technique to similarly speed up a sophisticated algorithm for solving 3-SAT. In this note, we show that a similar speed up can be obtained for all major record-breaking algorithms for satisfiability. We also show that if we use Grover's technique only, then we cannot do better than quadratic speed up.

Three dozen papers on online algorithms

Abstract: This column contains a summary of last year's research on online algorithms presented at the STOC, FOCS, ICALP, ESA, and STACS conferences. Unfortunately, due to space constraints, the report could not be entirely exhaustive, and results from other conferences or journal articles are not covered. We hope that all readers will find in the survey something of interest, to fill those long winter evenings. The papers in the report are organized roughly by applications.

On the definition of "on-line" in job scheduling problems

Abstract: The conventional model of on-line scheduling postulates that jobs have non-trivial release dates, and are not known in advance. However, it fails to impose any stability constraints, leading to algorithms and analyses that must deal with unrealistic load conditions arising from trivial release dates as a special case. In an effort to make the model more realistic, we show how stability can be expressed as a simple constraint on release times and processing times. We then give empirical and theoretical justifications that such a constraint can close the gap between the theory and practice. As it turns out, this constraint seems to trivialize the scheduling problem.

Review of "Data Structures, Near Neighbor Searches, and Methodology: Fifth and Sixth DIMACS Implementation Challenge by Michael H. Goldwasser, David S. Johnson, Catherine C. McGeoch", American Mathematical Society 2002

Abstract: 1 Overview This book is in the area of searching data structures, and algorithms. It also has a discussion on experimental analysis of algorithms. The goal of DIMACS Implementation Challenges is projected as to promote top quality experimental research on algorithms, and data structures. The fifth challenge (1995-1996) was on dictionaries, and priority queues. The first part of the book is from the works in the fifth challenge. The sixth challenge (1998) was on near neighbor searching. The second part of the book is from the works in the sixth challenge. The third part of the book has general discussion articles on algorithm experiments.

SIGACT news logic column 14

Abstract: For this issue, James Cheney describes nominal logic, an approach to solve the problems involved with reasoning about bindings in formal languages that has been gaining in popularity in recent years, and surveys its major application areas.

Algorithmic foundations of the internet

Abstract: In this paper we survey the field of Algorithmic Foundations of the Internet, which is a new area within theoretical computer science. We consider six sample topics that illustrate the techniques and challenges in this field.

The finite and the infinite in temporal logic

Abstract: At the last TACAS in Barcelona, already almost a year ago, Alur, Etessami, and Madhusudan [2004] introduced CaRet, a temporal logic framework for reasoning about programs with nested procedure calls and returns. The details of the logic were themselves interesting (I will return to them later), but a thought struck me during the presentation, whether an axiomatization might help understand the new temporal operators present in CaRet. Thinking a bit more about this question quickly led to further questions about the notion of finiteness and infinity in temporal logic as it is used in Computer Science. This examination of the properties of temporal logic operators under finite and infinite interpretations is the topic that I would like to discuss here. I will relate the discussion back to CaRet towards the end of the article, and derive a sound and complete axiomatization for an important fragment of the logic.

Review of "Immunocomputing: Principles and Applications by Alexander O. Tarakanov, Victor A. Skormin, Svetlana P. Sokolova", Springer-Verlag New York, Inc. 2003

Abstract: The natural immune system is a complex system with several mechanisms for defense against pathogenic organisms. From the perspective of information-processing, the main purpose of the immune system is to solve recognition and classification tasks, and categorize cells or molecules as self or non-self. It learns through evolution to distinguish between foreign antigens (e.g., bacteria, viruses) and the body’s own cells or molecules. The introduction argues that the immune system is much better understood than the nervous system.

Review of "Classical and Quantum Computing with C++ and Java Simulations, by Yorick Hardy and Willi-Hans Steeb", Birkhauser Verlag, 2001

Abstract: This textbook is an almost encyclop1⁄2dic tome on a range of topics mainly within the undergraduate computer science curriculum. Its coverage is very broad, starting from boolean algebra and proceeding all the way to implementations of quantum computers. The selection and ordering of topics is somewhat arbitrary, and a book could be written about the subject matter of nearly every chapter. The most distinctive feature of this text is its coverage of quantum computing. However, while the title may suggest a balanced treatment of classical and quantum computing, only 30% of the book's pages are devoted to the latter. One may wonder what the intended readership is, since there are several good texts devoted to quantum computing, and many many more on the topics covered in the other 400 pages. 2 c ° Nick Papanikolaou, 2005

Review of "Proofs that Really Count: The Art of Combinatorial Proof by Arthur T. Benjamin and Jennifer J. Quinn"; MAA, 2003

Abstract: Abbott: Costello, how many subsets are there of {1,. .. , n}? Costello: Oh. You can either choose 0 elements, or choose 1 element, or choose 2 elements, etc. So the answer is n i=0 n i. Abbott: Well. .. let me show you a different way to do it. The number 1 is either in the set A or not, so thats 2 choices. Then the number 2 is either in the set A or not, so thats 2 choices, etc. So the final answer is 2 × · · · × 2 = 2 n. So, Costello, you did the problem your way, I did it my way, and we got different answers. What can you conclude? Costello: That one of us is wrong? Abbott: No. We've shown. n i=0 n i = 2 n. Costello: (Ignoring reference) Usually when I do a math problem two ways and get two answers I assume one of them is wrong and try to find my error. Its better than what a friend of mine did in elementary algebra— do a problem three times and then take the average. Abbott: In math you can sometimes prove that two things are the same by solving the same problem two different ways.

SIGACT news logic column 13

Abstract: For this issue, Nick Papanikolaou brings us an introduction to the subject of quantum logic and a survey of the relevant literature, including a discussion of logics for specification and analysis of quantum information systems.

A note on turing machine computability of rule driven systems

Abstract: An abstract rule driven system is described. We prove that it is calculated by a restricted Turing Machine.

What should computer science students learn from mathematics

Abstract: There is an important difference between the title and "What Mathematics should Computer Science students learn?" This talk addresses both questions. To do so, it brings together some examples that illustrate the current state of computer science and information technology.

SIGACT news complexity theory column 49

Abstract: Warmest thanks to Neil Immerman for this issue's column, which is on Progress in Descriptive Complexity. (As you can see in this column, Neil is the rare writer whose italic lines truly deserve the italics.) This issue should reach your hands shortly before winter intersession, and I'd highly recommend that, if you don't already own Neil's wonderful book Descriptive Complexity ([I] in this column's bibliography), you consider visiting your school's library and bringing it home for holidays.

Kolmogorov complexity leads to a representation theorem for idempotent probabilities (σ-maxitive measures)

Abstract: In many application areas, it is important to consider maxitive measures (idempotent probabilities), i.e., mappings m for which m(A ∪ B) = max(m(A), m(B)). In his papers, J. H. Lutz has used Kolmogorov complexity to show that for constructively defined sets A, one maxitive measure - fractal dimension - can be represented as m(A) = sup f(x). We show that a similar representation is possible for an arbitrary maxitive measure.

The sets of real and complex numbers are denumerable

Abstract: This short article demonstrates that both the sets of real and complex numbers are actually denumerable, which means that those numeric sets, as well as the set of natural numbers, actually have the same cardinality, hence there exists a unique transfinite number.

The halting problem on finite and infinite computers

Abstract: This paper discusses some points originally raised by Robert L. Massey of Colorado, USA, and some consequences of that discussion. Firstly, earthly (ie. realistic) computers are finite because the number of atoms on Earth is finite. Secondly, and the main result of the paper is that, the famous Halting Problem is unsolvable only for infinite machines. In the end of the paper there are some thoughts about the consequences of these results, such as a suggestion to improve the classical Linear Bounded Automaton model.

Review of "Logic for Computer Scientists, by Uwe Schöning", Birkhauser, 1994

Abstract: Logic for Computer Scientists by Uwe Schöning $50.00, 175 pages, Hardcover Birkhauser, 1994 Review by Riccardo Pucella This is a short introductory book on the topic of propositional and first-order logic, with a bias towards computer scientists. What's a bias towards computer scientists, you ask? Good question. Despite my initial belief, it does not mean that it introduces logic with an eye towards the wide variety of areas where logic is used in computer science. Rather, it gives a computational perspective on logic; the emphasis is on computational aspects of logic, and specifically on procedures for establishing the satisfiability or unsatisfiability of formulas, culminating in various forms of the resolution procedure. (In that same sense, Smullyan [5] gives a tableaux-based perspective on firstorder logic.) The study of resolution procedures leads naturally to the topic of using predicate logic as a programming language, that is, logic programming. This focus on computational aspects means that there is much less coverage of those topics typically found in logic textbooks, such as axiomatization and completeness results, or model theoretic notions such as applications of compactness and theories. This is not a criticism, mind you: there are other good introductory books that deal with that. SchÄoning decides to concentrate on computational issues, and gives us a short book (less than 170 pages) with a tight storyline.

Review of "Integer Programming, by Laurence A. Wolsey", Wiley and Sons 1998

Abstract: Laurence A. Wolsey's book Integer Programming is one of the few books currently available which is dedicated to the subject of integer programming. As such, it is a very well written and comprehensive book on the subject, and is written in a manner which is friendly to those who are new to the subject. It is reminiscent of a good advanced mathematics textbook, as it comprehensively explains and proves its topics, as well as offering some examples and problems for the reader to solve. However, perhaps more due to the complexity of the subject matter itself rather than the ability of Wolsey to convey said subject matter, it is not an easy read for anyone interested in learning about Integer Programming. An appropriate audience would be graduate computer science students with a strong background in math and mathematical proofs using it as a course text, or postgraduates looking to learn the subject matter on their own. There are several prerequisites to reading the book that one should have in order to come away with a good understanding. The most basic need is for an understanding of mathematical notation and proofs, as they are (unsurprisingly) used throughout and often as explanations of themselves. One should also have a good grasp of linear algebra and topology of the real numbers, as they are both commonly used in the material and integral to the concepts explained. It is suggested that the reader have at least a basic understanding of linear programming as well, as several of the beginning and almost all of the later techniques and problems make use of it, and Wolsey does not explain how to solve such and uses some limited terminology related to the subject. Integer Programming is an in depth book. It is not a book intended to be a quick guide to integer programming techniques and applications and should not be taken as such. This book is intended to give a comprehensive understanding of the problems of integer programming and its related theories. The reader should come away from this book with an understanding of how to tackle problems related to integer programming, and also understand the complexity of the problems as well as the complexity, efficiency, and theories behind the techniques used to solve such problems. The material is comprehensive and not easy to take in though, and may require several re-readings in order to wholly understand some of the concepts presented.