Abstract
Graph partitioning is an important NP-complete problem with applications in VLSI CAD, processor allocation, and many other areas. The problem is to partition vertices of a graph into two equal-sized sets so that the number of edges joining the sets is minimal. In this paper we show that the Kernighan-Lin heuristic is P-complete and the simulated annealing heuristic is P-hard, which means that they are both hard to parallelize. We also describe a new parallel heuristic that on the 32K-processor CM-2 Connection Machine handles graphs with more than two million edges and gives in nine minutes partitions that are within 2% of the best ever found.
This work was supported in part by National Science Foundation under Grant CDA 87-22809 and the Office of Naval Research under contract N00014-83-K-0146 and ARPA Order No. 4786.
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Savage, J.E., Wloka, M.G. (1990). On parallelizing graph-partitioning heuristics. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032052
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DOI: https://doi.org/10.1007/BFb0032052
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