Abstract. 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.... more
Abstract. 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 “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/distributed (randomized) algorithms for such balanced versions. We also complement our algorithms with several lower bounds. Randomization plays a key role in our upper and lower bound results.
We show that the calculation of the well-known lower bound of Mingozzi for the RCPSP is an NP-hard problem and that the relative error of this lower bound can be equal to O(log n), where n is the number of jobs. 2