Minimum convex piecewise linear cost tension problem on quasi-k series-parallel graphs
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Some hypermedia synchronization issues request the resolution of the minimum convex piecewise linear cost tension problem (CPLCT problem) on directed graphs that are close to two-terminal series-parallel graphs (TTSP-graphs), the so-called quasi-k series-parallel graphs (k-QSP graphs). An aggregation algorithm has already been introduced for the CPLCT problem on TTSP-graphs. We propose here a reconstruction method, based on the aggregation and the well-known out-of-kilter techniques, to solve the problem on k-QSP graphs. One of the main steps being to decompose a graph into TTSP-subgraphs, methods based on the recognition of TTSP-graphs are thoroughly discussed.
Keywords:Minimum cost tension two-terminal series-parallel digraph graph decomposition series-parallel recognition out-of-kilter algorithm
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