Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
Theoretical Computer Science - Selected papers in honor of Manuel Blum
Divide-and-conquer approximation algorithms via spreading metrics
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Geometry of Cuts and Metrics
Decorous Lower Bounds for Minimum Linear Arrangement
INFORMS Journal on Computing
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We introduce flow metrics as a relaxation of path metrics (i.e. linear orderings). They are defined by polynomial-sized linear programs and have interesting properties including spreading. We use them to obtain relaxations for several NP-hard linear ordering problems such as minimum linear arrangement and minimum pathwidth. Our approach has the advantage of achieving the best-known approximation guarantees for these problems using the same relaxation and essentially the same rounding algorithm for all the problems while varying only the objective function from problem to problem. This is in contrast to the current state of the literature where each problem either has a new relaxation or a new rounding or both. We also characterize a natural projection of the flow polyhedron.