by Matthew Andrews, Lisa Zhang
http://cm.bell-labs.com/cm/ms/who/andrews/edp-congestion.ps
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Abstract:
NP nolog1?" In the Edge-Disjoint Paths problem with Congestion (EDPwC), we are given a graph withMedges and a set of terminal pairs. The objective is to route as many terminal pairs as possible subject to the constraint that at mostwdemands can be routed through any edge in the graph. In this paper, we study the hardness of EDPwC in undirected graphs. We show that for any constant">0and any congestionw=o(loglogM=logloglogM)there is w+1M-approximation algorithm for EDPwC, unless ZPTIME(npolylogn). For larger congestionsw loglogM=logloglogMfor some constant, we obtain superconstant inapproximability ratios. Our reduction makes use of the Raz verifier and builds upon the hardness for a related congestion minimization problem [1]. 1
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