A Parallel TSP-Based Algorithm for Balanced Graph Partitioning

We propose a heuristic for parallel partitioning of graphs into equi-sized components. In particular, we identify a relationship between the graph partitioning problem (GPP) and the traveling saleman problem (TSP), and use that to reduce partitioning to TSP. Given that better performing heuristics are known for TSP than are for GPP, this reduction also leads to improved GPP heuristics. What is more, a good GPP solution can also be used to speed up computation of TSP.We first derive a good bi-partition from a cut of the TSP cycle in time proportional to the number of edges in the graph. We then continue this bi-partitioning recursively until the required number of partitions are left. Further, in order to speed up the computation of TSP, which we use as a subroutine, we perform an initial rough partitioning of the graph into K parts, compute TSP tours in each of these smaller partitions and then merge these local tours to solve the full TSP.We then use this full TSP solution to obtain the final partitioning in parallel. Our empirical analysis shows that for partition count k ≽ 32, our parallel algorithm gives a cut better in size than that of algorithms known for low cut-size (e.g., KaBaPE), and when time is of concern, it finishes in significantly less time with comparable cuts. We also show that our algorithm gives much smaller cuts in comparable time than those known for fast computation (e.g., PT-Scotch).