Abstract
The budgeted colored matching problem (BCM) is a weighted matching problem on edge-colored graphs with additional edge costs. Budget constraints require the accumulated cost of same-colored edges not to exceed a corresponding specified budget. We show the strong NP-hardness of the BCM on bipartite graphs with uniform edge weights, costs and budgets using a reduction from (3,B2)-SAT. Subsequently, we propose a dynamic program for series-parallel graphs with pseudo-polynomial run time for a fixed number of budget constraints. As an extension we show how this algorithm can be used to solve the BCM on trees using a graph transformation.
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