We study leading-edge local search heuristics for balanced hypergraph partitioning and Boolean satisfiability, intending the generalization of such heuristics beyond their original domains. We adapt the Fiduccia Mattheyses (FM) hypergraph partitioning heuristic to Boolean Satisfiability (SAT), and the WalkSAT SAT solver to hypergraph partitioning. Focusing on balanced hypergraph partitioning, w...

Estimating the discrepancy of the hypergraph of all arithmetic progressions in the set [N ] = {1, 2, . . . , N} was one of the famous open problems in combinatorial discrepancy theory for a long time. An extension of this classical hypergraph is the hypergraph of sums of k (k ≥ 1 fixed) arithmetic progressions. The hyperedges of this hypergraph are of the form A1 + A2 + . . . + Ak in [N ], wher...

Using the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph, we continue the investigation of the existence of a decomposition of the complete 3-uniform hypergraph into Hamiltonian cycles began by Bailey and Stevens. We also discuss two extensions of the problem: to the complete 3-uniform hypergraph from which a parallel class of triples has been removed, and to the com...

The paper considers the problem of computing a maximal independent set in a hypergraph (see 3] and 7]). We present an eecient deterministic NC algorithm for nding a maximal independent set in a hypergraph of dimension 3: the algorithm runs in time O(log 4 n) time on n + m processors of an EREW PRAM and is optimal up to a polylogarithmic factor. Our algorithm adapts the technique of Goldberg and...

We introduce two new notions for hypergraphs, hypertree-depth and minors in hypergraphs. We characterise hypergraphs of bounded hypertree-depth by the ultramonotone robber and marshals game, by vertex-hyperrankings and by centred hypercolourings. Furthermore, we show that minors in hypergraphs are ‘well-behaved’ with respect to hypertree-depth and other hypergraph invariants, such as generalise...

Abstract As introduced in the previous chapters, complexity of hypergraph computation is relatively high. In practical applications, may not be a small scale, where we often encounter scenario that size very large. Therefore, confronts issues many applications. how to handle large scale data an important task. this chapter, discuss methods for hypergraphs and their Two types are provided data, ...