Load balancing for distributed branch & bound algorithms

Abstract

W e present a n e w load balancing strategy and its application t o distribuled branch 64 bound algorilhms and demonstrate its efficiency by solving some NPcomplete problems o n a network of u p t o 256 Transputers. T h e parallelizalion of our bran.ch & bound algorithm is fully distributed. Every processor performs the same algorithm but each o n a different part of the solution tree. I n ih,is case it is n,ecessary to distribute subproblems among the processors t o ach.ieve a well balanced workload. O u r load balancing method overcomes the problem of search overhead and idle limes by a n appropriate load model and avoids trashing effects by a feedback control method. Using this strategy we were able t o achieve a speedup of u p to 237.32 o n a 256 processor n.etwork for very short parallel computation times, com.pared t o an, efficien.t sequential alg orit h m .

Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture

“…It is difficult to compare the branch-and-bound algorithm to state-of-the-art algorithms [36,37] because they are usually tested on a different graph ensemble where each edge appears with a certain probability, independently of the graph size (high-connectivity regime). Nevertheless, in the literature usually graphs with up to 200 vertices are treated, which is slightly larger than the systems considered here.…”

The Liquid Model Load Balancing Method

“…For example, the diffusion was used for branch-and-bound algorithms on Intel iPSC/2 in [Willebeek90] and on Transputer clusters with de-Bruijn and ring topologies in [Lüling92].…”

ExactMP: An Efficient Parallel Exact Solver for Phylogenetic Tree Reconstruction Using Maximum Parsimony

“…Lüling and Monien [19] implemented a parallel B&B for the Vertex Cover problem and achieved a parallel speedup of 237.32 using a ring topology on a 256 processor system. Laursen [17] presents a parallel B&B for Quadratic Assignment, Graph Partitioning, and Weighted Vertex Cover problems and demonstrates a processor utilization factor of up to 0.954 through specialized communication protocols, such as Half-Surplus and On-Demand.…”