An extension of matching theory
Journal of Combinatorial Theory Series B
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Journal of Combinatorial Theory Series B
Short cycle covers and the cycle double cover conjecture
Journal of Combinatorial Theory Series B
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SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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ACM Transactions on Algorithms (TALG)
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
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ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Theoretical Computer Science
Strategic cooperation in cost sharing games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
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We define a problem called Simplex Matching, and show that it is solvable in polynomial time. While Simplex Matching is interesting in its own right as a nontrivial extension of non-bipartite min-cost matching, its main value lies in many(seemingly very different) problems that can be solved using ouralgorithm. For example, suppose that we are given a graph with terminal nodes, non-terminal nodes, and edge costs. Then, the Terminal Backup problem, which consists of finding the cheapest forest connecting every terminal to at least one other terminal, is reducible to Simplex Matching. Simplex Matching is also useful for various tasks that involve forming groups of at least two members, such as project assignment and variants of facility location. In an instance of Simplex Matching, we are given a hypergraphH with edge costs, and edge size at most 3. We show how to find the min-cost perfect matching of H efficiently, if the edge costs obey a simple and realistic inequality that we call the SimplexCondition. The algorithm we provide is relatively simple to understand and implement, but difficult to prove correct. In the process of this proof we show some powerful new results about covering cubic graphs with simple combinatorial objects.