1 1 Introduction 2 2 Related Work 5 3 Preliminaries 7 3.1 The Asynchronous Shared-Memory Model : : : : : : : : : : : : : : : : : : : 7 3.2 Sensitivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4 The Left/Right Algorithm 11 4.1 The General Scheme : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 4.2 The Left/Right Algorithm : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 4.2.1 Overview : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 4.2.2 The code : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 4.2.3 Correctness of the Algorithm : : : : : : : : : : : : : : : : : : : : : : 16 4.2.4 Analysis of the Algorithm : : : : : : : : : : : : : : : : : : : : : : : : 18 4.3 Inherently Asymmetric Data Structures : : : : : : : : : : : : : : : : : : : : 21 5 The Decision Algorithm 23 5.1 Monotone Paths : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 23 5.1.1 One Phase :...

This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as “how expensive is local verification? ” and more specifically “how expensive is local verification compared to computation? ” A suitable model is intro-duced in which these questions are studied in terms of the number of bits a node needs to communicate. In addition, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the cost of schemes for multiple basic prob-lems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables verification to be less costly, since the configu-ration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configu-ration without bothering with the need to verify, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algo-rithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.

We study combinatorial optimization problems in which a set of distributed agents must achieve a global objective using only local information. Papadimitriou and Yannakakis [15] initiated the study of such problems in a framework where distributed decision-makers must generate feasible solutions to positive linear programs with information only about local constraints. We extend their model by allowing these distributed decision-makers to perform local communication to acquire information over time and then explore the tradeo between the amount of communication and the quality of the solution to the linear program that the decision makers can obtain. Our main result is a distributed algorithm that obtains a (1 ) approximation to the optimal linear programming solution while using only a polylogarithmic number of rounds of local communication. This algorithm oers a signi cant improvement over the logarithmic approximation ratio previously obtained by [3] for this problem while prov...

This paper describes the invited talk given at the 8th International

This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as “how expensive is local verification?” and more specifically “how expensive is local verification compared to computation?” A suitable model is introduced in which these questions are studied in terms of the number of bits a node needs to communicate. In particular, it is shown that the cost of verification is sometimes rather high, even higher than the number of bits needed for a computation. On the other hand, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the cost of schemes for multiple basic problems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables verification to be less costly, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.