HOWGOODISRECURSIVEBISECTION.PDFVIP

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HOWGOODISRECURSIVEBISECTION.PDF

c SIAM J SCIENT COMP So ciety for Industrial and Applied Mathematics Vol xx No x pp to app ear HOW GOOD IS RECURSIVE BISECTION HORST D SIMON AND SHANGHUA TENG y Abstract The most commonly used pway partitioning metho d is recursive bisection RB It rst divides a graph or a mesh into two equal sized pieces by a go o d bisection algorithm and then recursively divides the two pieces Ideally we would like to use an optimal bisection algorithm Because the optimal bisection problem that partitions a graph into two equal sized subgraphs to minimize the numb er of edges cut is NPcomplete practical RB algorithms use more ecient heuristics in place of an optimal bisection algorithm Most such heuristics are designed to nd the b est p ossible bisection within allowed time We show that the recursive bisection metho d even when an optimal bisection algorithm is assumed may pro duce a pway partition that is very far way from the optimal one Our negative result is complemented by two p ositive ones First we show that for some imp ortant classes of graphs that o ccur in practical applications such as wellshap ed nite element and nite dierence meshes RB is within a constant factor of the optimal one almost always Secondly we show that if the balance condition is relaxed so that each blo ck in the pway partition is b ounded by np where n is the numb er of vertices of the graph then a mo died RB nds an approximately balanced pway partition whose cost is within an O log p factor of the cost of the optimal pway partition Key words Communication cost data and computation mapping on parallel machines load balancing mesh partitioning parallel pro cessing recursive

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