Distributed Computing: A Locality-Sensitive Approach by David Peleg

By David Peleg

This quantity offers the locality-sensitive method of disbursed community algorithms-the usage of locality to simplify regulate buildings and algorithms and decrease their charges. the writer starts off with an introductory exposition of allotted community algorithms concentrating on themes that illustrate the function of locality in dispensed algorithmic thoughts. He then introduces locality-preserving community representations and describes sequential and allotted concepts for his or her building. eventually, the applicability of the locality-sensitive method is tested via a number of purposes.

Distributed Computing: A Locality-Sensitive process is the one publication that provides an intensive exposition of community spanners and different locality-preserving community representations reminiscent of sparse covers and walls. The ebook turns out to be useful for computing device scientists drawn to disbursed computing, electric engineers drawn to community architectures and protocols, and for discrete mathematicians and graph theorists.

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Extra resources for Distributed Computing: A Locality-Sensitive Approach (Monographs on Discrete Mathematics and Applications)

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Formally, the problem of broadcast from a single source can be stated as follows. 1 [Broadcast]: The broadcast operation is initiated by a single processor TQ, called the source. The source has a message, initially kept on a special input buffer. This message needs to be disseminated from the source to all vertices in the network. We observe the following simple global lower bounds for the complexity of the broadcast operation. 2 For any broadcast algorithm B and any n-vertex network G, Message(5,G) > n — 1 and ~T\me(B,G) > Rad(ro,G) = fl(Diam(G)), in either the synchronous or the asynchronous model.

Formally, the problem of broadcast from a single source can be stated as follows. 1 [Broadcast]: The broadcast operation is initiated by a single processor TQ, called the source. The source has a message, initially kept on a special input buffer. This message needs to be disseminated from the source to all vertices in the network. We observe the following simple global lower bounds for the complexity of the broadcast operation. 2 For any broadcast algorithm B and any n-vertex network G, Message(5,G) > n — 1 and ~T\me(B,G) > Rad(ro,G) = fl(Diam(G)), in either the synchronous or the asynchronous model.

The basic message length is assumed to be O(logn) bits. , a message of length L > logn is viewed as flo^n"! basic messages). 4 [Message complexity]: The message cost of transmitting a basic message over an edge is 1. , over every legal input for II on G and in every execution scenario). 4 Weighted cost measures for communication tasks The efficiency of communication in a computer network critically depends on the delays existing on the various links at any given moment. These delays, caused by high traffic loads of currently transmitted and queued messages, are usually modeled in communication network theory by representing the network as a weighted graph G = (V,E,u>), where a positive weight u(e) is associated with each edge of the graph.

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