This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our novel randomized partitioning scheme, runs the centralized algorithm on each partition separately, and then stitches the resulting solutions to produce a globa...

A k-factor of a graph G = (V (G), E(G)) is a k-regular spanning subgraph of G. A k-factorization is a partition of E(G) into k-factors. If V 1 , ..., V p are the p parts of V (K(n, p)) (the complete multipartite graph with p parts, each of size n), then a holey k-factor of deficiency V i of K(n, p) is a k-factor of K(n, p) − V i for some i satisfying 1 ≤ i ≤ p. Hence a holey k-factorization is ...

We introduce a new form of game search called partition search that incorporates dependency analysis, allowing substantial reductions in the portion of the tree that needs to be expanded. Both theoretical results and experimental data are presented. For the game of bridge, partition search provides approximately as much of an improvement over existing methods as a-0 pruning provides over minimax.

Let F = (Kn,P) be a circulant homogeneous factorisation of index k, that means P is a partition of the arc set of the complete digraph Kn into k circulant factor digraphs such that there exists σ ∈ Sn permuting the factor circulants transitively amongst themselves. Suppose further such an element σ normalises the cyclic regular automorphism group of these circulant factor digraphs, we say F is ...

In this paper, we characterize planar point sets that can be partitioned into disjoint polygons of arbitrarily specified sizes. We provide an algorithm to construct such a partition, if it exists, in polynomial time. We show that this problem is equivalent to finding a specified 2-factor in the visibility graph of the point set. The characterization for the case where all cycles have length 3 a...

A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...

We introduce partition equilibrium and study its existence in resource selection games (RSG). In partition equilibrium the agents are partitioned into coalitions, and only deviations by the prescribed coalitions are considered. This is in difference to the classical concept of strong equilibrium according to which any subset of the agents may deviate. In resource selection games, each agent sel...

One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This classification is based on a beautiful connection to the so-called uniqueness phase transition from statistical physics on the infinite ∆-regular tree. Our objec...

Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely partition-distance D(·, ·). The comparison achieves by checking their restriction to modular elements of the partition lattice, as well as in terms of suitable classifiers. Two of the new measures obtain through the size, a function mapping every ...

where the LGLn(λ) are irreducible GLn(C)-modules and the S λ k are irreducible Sk-modules. The decomposition in (0.1) essentially makes the study of the representations of GLn(C) and the study of representations of the symmetric group Sk two sides of the same coin. The group GLn(C) has interesting subgroups, GLn(C) ⊇ On(C) ⊇ Sn ⊇ Sn−1, and corresponding centralizer algebras, CSk ⊆ CBk(n) ⊆ CAk(...