This paper focuses on showing timemessage tradeoffs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems. We consider the synchronous CONGEST distributed computing model and assume that each node has initial knowledge of itself and the identifiers of its neighbors  the socalled KT_1 model  a wellstudied model that also naturally arises in many applications. Recently, it has been established that one can obtain (almost) singularly optimal algorithms, i.e., algorithms that have simultaneously optimal time and message complexity (up to polylogarithmic factors), formore »
Asynchronous Local Construction of BoundedDegree Network Topologies Using Only Neighborhood Information
We consider the adhoc networks consisting of n wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be directly connected to any one of its neighbors, and picks its connections according to a unique topology control algorithm that is available at every node. Given that each node knows only the indices (unique identification numbers) of its one and twohop neighbors, we identify an algorithm that preserves connectivity and can operate without the need of any synchronization among nodes. Moreover, the algorithm results in a sparse graph with at most 5n edges and a maximum node degree of 10. Existing algorithms with the same promises further require neighbor distance and/or direction information at each node. We also evaluate the performance of our algorithm for random networks. In this case, our algorithm provides an asymptotically connected network with n(1+o(1)) edges with a degree less than or equal to 6 for 1o(1) fraction of the nodes. We also introduce another asynchronous connectivitypreserving algorithm that can provide an upper bound as well as a lower bound on node degrees.
 Award ID(s):
 1814717
 Publication Date:
 NSFPAR ID:
 10118984
 Journal Name:
 IEEE transactions on communications
 Volume:
 67
 Issue:
 3
 Page Range or eLocationID:
 21012113
 ISSN:
 15580857
 Sponsoring Org:
 National Science Foundation
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