Johnson: Computers and Intractability-A Guide to the Theory of NP-Completeness

From the Publisher:
With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter.


0201000296B04062001

The Design and Analysis of Computer Algorithms

In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers.



Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others.



The material is organized according to the system model-first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference.



The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.


Table of Contents

1 Introduction 
2 Modelling I; Synchronous Network Model 
3 Leader Election in a Synchronous Ring 
4 Algorithms in General Synchronous Networks 
5 Distributed Consensus with Link Failures 
6 Distributed Consensus with Process Failures 
7 More Consensus Problems 
8 Modelling II: Asynchronous System Model 
9 Modelling III: Asynchronous Shared Memory Model 
10 Mutual Exclusion 
11 Resource Allocation 
12 Consensus 
13 Atomic Objects 
14 Modelling IV: Asynchronous Network Model 
15 Basic Asynchronous Network Algorithms 
16 Synchronizers 
17 Shared Memory versus Networks 
18 Logical Time 
19 Global Snapshots and Stable Properties 
20 Network Resource Allocation 
21 Asynchronous Networks with Process Failures 
22 Data Link Protocols 
23 Partially Synchronous System Models 
24 Mutual Exclusion with Partial Synchrony 
25 Consensus with Partial Synchrony

Distributed algorithms

We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least.87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of 1/2 for MAX CUT and 3/4 or MAX 2SAT. Slight extensions of our analysis lead to a.79607-approximation algorithm for the maximum directed cut problem (MAX DICUT) and a.758-approximation algorithm for MAX SAT, where the best previously known approximation algorithms had performance guarantees of 1/4 and 3/4, respectively. Our algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.

/pdf/improved-approximation-algorithms-for-maximum-cut-and-3utsb8qos4.pdf

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

We propose a novel paradigm for defining security of cryptographic protocols, called universally composable security. The salient property of universally composable definitions of security is that they guarantee security even when a secure protocol is composed of an arbitrary set of protocols, or more generally when the protocol is used as a component of an arbitrary system. This is an essential property for maintaining security of cryptographic protocols in complex and unpredictable environments such as the Internet. In particular, universally composable definitions guarantee security even when an unbounded number of protocol instances are executed concurrently in an adversarially controlled manner, they guarantee non-malleability with respect to arbitrary protocols, and more. We show how to formulate universally composable definitions of security for practically any cryptographic task. Furthermore, we demonstrate that practically any such definition can be realized using known techniques, as long as only a minority of the participants are corrupted. We then proceed to formulate universally composable definitions of a wide array of cryptographic tasks, including authenticated and secure communication, key-exchange, public-key encryption, signature, commitment, oblivious transfer, zero knowledge and more. We also make initial steps towards studying the realizability of the proposed definitions in various settings.

/pdf/universally-composable-security-a-new-paradigm-for-3kyhnjofve.pdf

Universally composable security: a new paradigm for cryptographic protocols

Some simplified NP-complete graph problems

The concept of partial synchrony in a distributed system is introduced. Partial synchrony lies between the cases of a synchronous system and an asynchronous system. In a synchronous system, there is a known fixed upper bound D on the time required for a message to be sent from one processor to another and a known fixed upper bound P on the relative speeds of different processors. In an asynchronous system no fixed upper bounds D and P exist. In one version of partial synchrony, fixed bounds D and P exist, but they are not known a priori. The problem is to design protocols that work correctly in the partially synchronous system regardless of the actual values of the bounds D and P. In another version of partial synchrony, the bounds are known, but are only guaranteed to hold starting at some unknown time T, and protocols must be designed to work correctly regardless of when time T occurs. Fault-tolerant consensus protocols are given for various cases of partial synchrony and various fault models. Lower bounds that show in most cases that our protocols are optimal with respect to the number of faults tolerated are also given. Our consensus protocols for partially synchronous processors use new protocols for fault-tolerant “distributed clocks” that allow partially synchronous processors to reach some approximately common notion of time.

/pdf/consensus-in-the-presence-of-partial-synchrony-2hgtwz8yrq.pdf

Consensus in the presence of partial synchrony

The polynomial-time hierarchy☆

Reaching agreement is a primitive of distributed computing. Whereas this poses no problem in an ideal, failure-free environment, it imposes certain constraints on the capabilities of an actual system: A system is viable only if it permits the existence of consensus protocols tolerant to some number of failures. Fischer et al. have shown that in a completely asynchronous model, even one failure cannot be tolerated. In this paper their work is extended: Several critical system parameters, including various synchrony conditions, are identified and how varying these affects the number of faults that can be tolerated is examined. The proofs expose general heuristic principles that explain why consensus is possible in certain models but not possible in others.

Larry J. Stockmeyer

Papers

Some simplified NP-complete graph problems

Consensus in the presence of partial synchrony

The polynomial-time hierarchy☆

On the minimal synchronism needed for distributed consensus

The equivalence problem for regular expressions with squaring requires exponential space