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A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds su ..."
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Cited by 390 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.
NearCritical Path Analysis of Program Activity Graphs
, 1994
"... Program activity graphs can be constructed from timestamped traces of appropriate execution events. Information about the activities on the k longest execution paths is useful in the analysis of parallel program performance. In this paper, four algorithms for finding the nearcritical paths of prog ..."
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Cited by 7 (3 self)
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Program activity graphs can be constructed from timestamped traces of appropriate execution events. Information about the activities on the k longest execution paths is useful in the analysis of parallel program performance. In this paper, four algorithms for finding the nearcritical paths of program activity graphs are presented and compared, including an efficient new algorithm that utilizes slack values calculated by the critical path method to perform a bestfirst search in linear space. The worstcase time and memory requirements of the new algorithm are in O(ke) and O(k+e), where e is the number of edges in the graph. Results confirming the efficiency of the algorithm are presented for five application programs. A framework for utilizing the nearcritical path information is also described. The framework includes both statistical summaries and visualization capabilities. Index TermsCritical path, program activity graph, instrumentation, parallel program performance analy...