Efficient Computation of Balanced Structures

Abstract

Basic graph structures such as maximal independent sets (MIS's) have spurred much theoretical research in 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: For example, in a star-graph, the central vertex, as well as the set of leaves, are both MIS's, with the latter being much more fault-tolerant and -- existing distributed algorithms do not handle this distinction. We propose and study low-average degree or balanced versions of such structures. Interestingly, in sharp contrast to, say, MIS's, it can be shown that checking whether a structure is balanced, will take substantial time. Nevertheless, we are able to develop good sequential and distributed algorithms for such balanced versions. We also complement our algorithms with several lower bounds.