Efficient computation of sparse structures

David G. Harris, Ehab Morsy, Gopal Pandurangan, Peter Robinson, Aravind Srinivasan

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Basic graph structures such as maximal independent sets (MIS's) have spurred much theoretical research in randomized and distributed algorithms, and have several applications in networking and distributed computing as well. However, the extant (distributed) algorithms for these problems do not necessarily guarantee fault-tolerance or load-balance properties. We propose and study “low-average degree” or “sparse” versions of such structures. Interestingly, in sharp contrast to, say, MIS's, it can be shown that checking whether a structure is sparse, will take substantial time. Nevertheless, we are able to develop good sequential/distributed (randomized) algorithms for such sparse versions. We also complement our algorithms with several lower bounds. Randomization plays a key role in our upper and lower bound results.
Original languageEnglish
Pages (from-to)322-344
Number of pages23
JournalRandom Structures and Algorithms
Issue number2
Early online date4 Apr 2016
Publication statusPublished - Sept 2016

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