A proof of the Boyd-Carr conjecture
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improving christofides' algorithm for the s-t path TSP
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the integrality gap of the subtour LP for the 1,2-TSP
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
The minimum spanning tree problem with non-terminal set
Information Processing Letters
Reordering rows for better compression: Beyond the lexicographic order
ACM Transactions on Database Systems (TODS)
A rounding by sampling approach to the minimum size k-arc connected subgraph problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Eight-Fifth approximation for the path TSP
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
An information complexity approach to extended formulations
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Guest column: the elusive inapproximability of the TSP
ACM SIGACT News
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For some positive constant \eps_0, we give a (3/2-\eps_0)-approximation algorithm for the following problem: given a graph G_0=(V,E_0), find the shortest tour that visits every vertex at least once. This is a special case of the metric traveling salesman problem when the underlying metric is defined by shortest path distances in G_0. The result improves on the 3/2-approximation algorithm due to Christofides [C76] for this special case. Similar to Christofides, our algorithm finds a spanning tree whose cost is upper bounded by the optimum, then it finds the minimum cost Eulerian augmentation (or T-join) of that tree. The main difference is in the selection of the spanning tree. Except in certain cases where the solution of LP is nearly integral, we select the spanning tree randomly by sampling from a maximum entropy distribution defined by the linear programming relaxation. Despite the simplicity of the algorithm, the analysis builds on a variety of ideas such as properties of strongly Rayleigh measures from probability theory, graph theoretical results on the structure of near minimum cuts, and the integrality of the T-join polytope from polyhedral theory. Also, as a byproduct of our result, we show new properties of the near minimum cuts of any graph, which may be of independent interest.