NDLI: On earthmover distance, metric labeling, and 0-extension

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On earthmover distance, metric labeling, and 0-extension

Content Provider	ACM Digital Library
Author	Mehta, Aranyak Rabani, Yuval Karloff, Howard Khot, Subhash
Abstract	We study the fundamental classification problems O-EXTENSION and METRIC LABELING. MINIMUM WEIGHT TRIANGULATION is closely related to partitioning problems in graph theory and to Lipschitz extensions in Banach spaces; its generalization METRIC LABELING is motivated by applications in computer vision. Researchers had proposed using earthmover metrics to get polynomial time-solvable relaxations for these problems. A conjecture that has attracted much attention recently is that the integrality ratio for these relaxations is constant.We prove that the integrality ratio of the earthmover relaxation for METRIC LABELING is Ω(log n) (which is asymptotically tight), k being the number of labels, whereas the best previous lower bound on the integrality ratio was only constant; that the integrality ratio of the earthmover relaxation for O-EXTENSION is Ω(√log k), k being the number of terminals (it was known to be O((log k)/log log k)), whereas the best previous lower bound was only constant; that for no ε>0 is there a polynomial-time O((log $n)^{1/4-ε})-approximation$ algorithm for O-EXTENSION, n being the number of vertices, unless NP ⊆ DTIME(npoly(log n)), whereas the strongest inapproximability result known before was only MAX SNP-hardness; and that there is a polynomial-time approximation algorithm for O-EXTENSION with performance ratio O(√diam(d)), where diam(d) is the ratio of the largest to smallest nonzero distances in the terminal metric.
Starting Page	547
Ending Page	556
Page Count	10
File Format	PDF
ISBN	1595931341
DOI	10.1145/1132516.1132595
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-05-21
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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