Impact of overlay properties upon a P2P approach for parallel B&B

The state-of-the-art large scale approach for solving NP-hard permutation-like problems using parallel Branch-and-Bound (B&B) techniques is based on a Master-Slave model which is known to be limited in terms of scalability. To overcome this limitation, we designed a Peer-to-Peer (P2P) approach that can handle a huge amount of computational resources in a fully distributed way, that is without the need of any centralized coordinator. The operation of such a decentralized parallel algorithm relies mainly upon the communications between the computational entities. Thus, the network overlay shall have an impact on the performances of the approach. In this paper, we study this impact through selecting some state-of-the-art topologies and through experimenting our protocol using these topologies. Results show that (1) our approach has a globally improved scalability, (2) it performs at best with topologies offering a good trade-off between the diameter and the average degree of the nodes, (3) our approach performs well using topologies presenting simple structures like N-ary trees and random graphs, which is a good indication for evolving towards dynamic environments, where computational entities can join or leave the network at any time.