Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [4, 26]. From the early work it was clear that multilevel techniques held great promise; however, it was not known if they can be made to...

In this brief note, we give two partition statistics which explain the following partition congruences: b(5n + 4) ≡ 0 (mod 5), b(7n + a) ≡ 0 (mod 7), if a = 2, 3, 4, or 6. Here, b(n) is the number of 4-color partitions of n with colors r, y, o, and b subject to the restriction that the colors o and b appear only in even parts.

We study the problem of approximately evaluating the independent set polynomial of boundeddegree graphs at a point λ. Equivalently, this problem can be reformulated as the problem of approximating the partition function of the hard-core model with activity λ on graphs G of maximum degree ∆. For λ > 0, breakthrough results of Weitz and Sly established a computational transition from easy to hard...

Multicore shared cache processors pose a challenge for designers of embedded systems who try to achieve minimal and predictable execution time of workloads consisting of several jobs. To address this challenge the cache is statically partitioned among the cores and the jobs are assigned to the cores so as to minimize the makespan. Several heuristic algorithms have been proposed that jointly dec...

In this paper we study some additive properties of subsets of N : A subset A of N is called ksummable (k a positive integer) if A contains {n∈F xn |F ⊆ {0, . . . , k − 1}} for some k-term sequence of natural numbers x0 < x1 < x2 < · · · < xk−1. We say A ⊆ N is FS big if A is k-summable for each positive integer k. We say is A ⊆ N is infinite FS big if for each positive integer k, A contains {n∈...

In this paper we present experiments with a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph. We investigate the effectiveness of many different choices for all three phases: coarsening, partition of the coarsest graph, and refinement. In p...