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Additive Guarantees for Degree Bounded Directed Network Design
 STOC'08
, 2008
"... We present polynomialtime approximation algorithms for some degreebounded directed network design problems. Our main result is for intersecting supermodular connectivity with degree bounds: given a directed graph G = (V, E) with nonnegative edgecosts, a connectivity requirement specified by an in ..."
Abstract

Cited by 22 (2 self)
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We present polynomialtime approximation algorithms for some degreebounded directed network design problems. Our main result is for intersecting supermodular connectivity with degree bounds: given a directed graph G = (V, E) with nonnegative edgecosts, a connectivity requirement specified by an intersecting supermodular function f, and upper bounds {av, bv}v∈V on indegrees and outdegrees of vertices, find a minimumcost fconnected subgraph of G that satisfies the degree bounds. We give a bicriteria approximation algorithm that for any 0 ≤ ɛ ≤ 1, computes an fconnected sub2 graph with indegrees at most ⌈ av ⌉+4, outdegrees at most
Approximating directed weighteddegree constrained networks
"... Keywords: Directed network design; Intersecting supermodular requirements; Weighted degree constraints; Bicriteria approximation algorithms. Given a graph ..."
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Cited by 8 (5 self)
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Keywords: Directed network design; Intersecting supermodular requirements; Weighted degree constraints; Bicriteria approximation algorithms. Given a graph
ADDITIVE GUARANTEES FOR DEGREEBOUNDED DIRECTED NETWORK DESIGN
, 2009
"... We present polynomialtime approximation algorithms for some degreebounded directed network design problems. Our main result is for intersecting supermodular connectivity requirements with degree bounds: given a directed graph G =(V, E) with nonnegative edgecosts, a connectivity requirement specif ..."
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Cited by 6 (1 self)
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We present polynomialtime approximation algorithms for some degreebounded directed network design problems. Our main result is for intersecting supermodular connectivity requirements with degree bounds: given a directed graph G =(V, E) with nonnegative edgecosts, a connectivity requirement specified by an intersecting supermodular function f, and upper bounds {av,bv}v∈V on indegrees and outdegrees of vertices, find a minimumcost fconnected subgraph of G that satisfies the degree bounds. We give a bicriteria approximation algorithm for this problem using the natural LP relaxation and show that our guarantee is the best possible relative to this LP relaxation. We also obtain similar results for the (more general) class of crossing supermodular requirements. In the absence of edgecosts, our result gives the first additive O(1)approximation guarantee for degreebounded intersecting/crossing supermodular connectivity problems. We also consider the minimum crossing spanning tree problem: Given an undirected edgeweighted graph G, edgesubsets {Ei} k i=1, and nonnegative integers {bi} k i=1, find a minimumcost spanning tree (if it exists) in G that contains at most bi edges from each set Ei. We obtain a +(r−1) additive approximation for this problem, when each edge lies in at most r sets. A special case of this problem is the degreebounded minimum spanning tree, and our techniques give a substantially shorter proof of