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

http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

A sequence a,, a,, . . . , a, of real numbers is said to be unimodal if for some 0 s j _c n we have a, 5 a , 5 . . 5 ai 2 a,,, 2 . . 2 a,, and is said to be logarithmically concave (or log-concave for short) if a: 2 a, ,a ,+ , for all 1 5 i 5 n 1. Clearly a log-concave sequence of positive terms is unimodal. Let us say that the sequence a,, a,, . . . , a, has no internal zeros if there do not exist integers 0 5 i < j < k 5 n satisfying a, f 0, a, = 0, ak # 0. Then in fact a nonnegative log-concave sequence with no internal zeros is unimodal. The sequence a,, a , , . . . , a, is called symmetric if a, = a,-, for 0 5 i 5 n. Thus a symmetric unimodal sequence a,, a, , . . . , a,, has its maximum at the middle term ( n even) or middle two terms (n odd). We also say that a polynomial a, + a,4 +. . + an$ has a certain property (such as unimodal, log-concave, or symmetric) if its sequence a,, a,, . . . , a, of coefficients has that property. Our object here is to survey the surprisingly rich variety of methods for showing that a sequence is log-concave or unimodal. For each method we will give examples of its applicability to combinatorially defined sequences that arise naturally from problems in algebra, combinatorics, and geometry. We make no attempt, however, to give a comprehensive account of all work done in this area.

Log‐Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry

Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions.

Two-Sided Matching

Preliminary Definitions, Results and Motivation Stable Matching Problems: The Stable Marriage Problem: An Update SM and HR with Indifference The Stable Roommates Problem Further Stable Matching Problems Other Optimal Matching Problems: Pareto Optimal Matchings Popular Matchings Profile-Based Optimal Matchings.

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Algorithmics of Matching Under Preferences

A board$\mathcal{B}$ is a finite set of unit squares lying in the plane whose corners have integer coordinates. A rectangle of $\mathcal{B}$ is a rectangular subset of $\mathcal{B}$ and an antirectangle is a set of squares in $\mathcal{B}$ no two of which are in a common rectangle. We prove a conjecture of Chvatal that $\mathcal{B}$ if is convex in the horizontal and vertical directions, then the minimum number of rectangles whose union is $\mathcal{B}$ equals the maximum cardinality of an antirectangle. Our proof uses two analogous minimax theorems about covering the corners and covering the edges of the board.We quote examples that illustrate the necessity of the hypotheses, and give some conjectures and open questions. The method of proof can give a polynomial running time algorithm for finding a minimum cover.

Covering Regions by Rectangles

Searching ordered structures

Presents an efficient distributed online algorithm for scheduling jobs that are created dynamically, subject to resource constraints that require that certain pairs of jobs not run concurrently. The focus is on the response time of the system to each job, i.e. the length of the time interval that starts when the job is created or assigned to a processor and ends at the instant the execution of the job begins. The goal is to provide guarantees on the response time to each job j in terms of the density of arrivals of jobs that conflict with j. The model is completely asynchronous and includes various resource allocation problems that have been studied extensively, including the dining philosophers problem and its generalizations to arbitrary networks. In these versions of the problem, the resource requirements of each new job j determines an upper bound delta /sub j/ on the number of jobs that can exist concurrently in the system and conflict with j. Given such upper bounds, no scheduling algorithm can guarantee a response time better than delta /sub j/ times the maximum execution or message transmission time. A simple algorithm that guarantees response time that is essentially polynomial in delta /sub j/ is presented. It is based on the notion of a distribution queue and has a compact implementation. >

A dining philosophers algorithm with polynomial response time

This paper introduces a new distributed data object called Resource Controller that provides an abstraction for managing the consumption of a global resource in a distributed system. Examples of resources that may be managed by such an object include; number of messages sent, number of nodes participating in the protocol, and total CPU time consumed.The Resource Controller object is accessed through a procedure that can be invoked at any node in the network. Before consuming a unit of resource at some node, the controlled algorithm should invoke the procedure at this node, requesting a permit or a rejection.The key characteristics of the Resource Controller object are the constraints that it imposes on the global resource consumption. An (M, W)-Controller guarantees that the total number of permits granted is at most M; it also ensures that, if a request is rejected, then at least M—W permits are eventually granted, even if no more requests are made after the rejected one.In this paper, we describe several message and space-efficient implementations of the Resource Controller object. In particular, we present an (M, W)-Controller whose message complexity is O(n log2n log(M/(W + 1)) where n is the total number of nodes. This is in contrast to the O(nM) message complexity of a fully centralized controller which maintains a global counter of the number of granted permits at some distinguished node and relays all the requests to the node.

/pdf/local-management-of-a-global-resource-in-a-communication-3t18n5gco0.pdf

Michael Saks

Papers

Covering Regions by Rectangles

Searching ordered structures

A dining philosophers algorithm with polynomial response time

Local management of a global resource in a communication network

A short proof of the existence of k-saturated partitions of partially ordered sets