Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved results for directed multicut
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating Directed Multicuts
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An O(n)-approximation algorithm for directed sparsest cut
Information Processing Letters
Hardness of cut problems in directed graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Polynomial flow-cut gaps and hardness of directed cut problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Improved approximation for directed cut problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Polynomial flow-cut gaps and hardness of directed cut problems
Journal of the ACM (JACM)
Local partitioning for directed graphs using PageRank
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
An experimental comparison of real and artificial deception using a deception generation model
Decision Support Systems
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The theory of embeddings of finite metrics has provided a powerful toolkit for graph partitioning problems in undirected graphs. The connection comes from the fact that the integrality gaps of mathematical programming relaxations for sparsest cut in undirected graphs is exactly equal to the minimum distortion required to embed certain metrics into l1. No analog of this metric embedding theory exists for directed (asymmetric) metrics, the natural distance functions that arise in considering mathematical relaxations for directed graph partioning problems. We initiate a study of metric embeddings for directed metrics, motivated by understanding directed variants of sparsest cut.It turns out that there are two different ways to formulate sparsest cut in directed graphs (depending on whether one insists on partitioning the graph into two pieces or not). Different subclasses of directed metrics arise in the consideration of mathematical relaxations for these two formulations and the embedding questions that result are quite different. Unlike in the undirected case, where the natural host space is l1, the host space in the directed case is not obvious and depends on the problem formulation. Our work is a first step at understanding this space of directed metrics, the resulting embedding questions and their relationships to directed graph partitioning problems.