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## Approximate Classification via Earthmover Metrics (2004)

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Venue: | In SODA ’04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms |

Citations: | 20 - 3 self |

### Citations

2120 | R.: Fast approximate energy minimization via graph cuts - Boykov, Veksler, et al. |

1278 | Approximation Algorithms - Vazirani - 2003 |

356 | Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms - Leighton, Rao - 1999 |

351 | Probabilistic approximation of metric spaces and its algorithmic applications. - Bartal - 1996 |

306 | A tight bound on approximating arbitrary metrics by tree metrics,”
- Fakcharoenphol, Rao, et al.
- 2004
(Show Context)
Citation Context ... case of a uniform metric on the labels, and combined this with Bartal’s probabilistic tree embeddings [Bar98] to obtain an O(log k log log k)-approximation for general metrics. Fakcharoenphol et al=-=. [FRT03] r-=-ecently improved Bartal’s result, leading to an improved bound of O(log k). The earthmover LP was proposed independently by Charikar [Cha00] and by Chekuri et al. [CKNZ01]. The first successful use ... |

266 | On approximating arbitrary metrices by tree metrics.
- Bartal
- 1999
(Show Context)
Citation Context ...n on truncated line metrics. Kleinberg and Tardos [KT02] gave a 2-approximation algorithm for the case of a uniform metric on the labels, and combined this with Bartal’s probabilistic tree embedding=-=s [Bar98] t-=-o obtain an O(log k log log k)-approximation for general metrics. Fakcharoenphol et al. [FRT03] recently improved Bartal’s result, leading to an improved bound of O(log k). The earthmover LP was pro... |

210 | Markov random fields with efficient approximations,” - Boykov, Veksler, et al. - 1998 |

208 | Efficient matching of pictorial structures,”
- Felzenszwalb, Huttenlocher
- 2000
(Show Context)
Citation Context ... then our approximation guarantee is worse than the O(log k) currently known. However, there are applications where k ≫ n. For instance, in recognizing the position of a human body from an image (se=-=e [FH00]-=-), the objects are the handful of rigid moving parts, and each part needs to be labeled with a six-tuple representing position, rotation and scale. 4 Our new algorithm for metric labeling uses the ear... |

197 | Approximation algorithms for classification problems with pairwise relationships: Metric labeling and markov random fields.
- Kleinberg, Tardos
- 1999
(Show Context)
Citation Context ...Y 14853. Research supported in part by NSF grant CCR0113371. Email: eva@cs.cornell.edu Kunal Talwar ¶ Éva Tardos � 1 Introduction The metric labeling problem has been proposed by Kleinberg and Tar=-=dos [KT02]-=- to model classification problems from several domains, ranging from categorizing web documents to machine vision, including image recovery and the stereo matching problem. Metric labeling models situ... |

194 | The complexity of multiterminal cuts,” - Dahlhaus, Johnson - 1994 |

136 | Sparse partitions. - Awerbuch, Peleg - 1990 |

121 | Excluded minors, network decomposition, and multicommodity flow.
- Klein, Plotkin, et al.
- 1993
(Show Context)
Citation Context ...omposable. It is wellknown (see [AP90, LR99, LS93]) that any graph on n vertices is O(log n)-decomposable, and that for some graphs (expanders) this bound is the best possible. Klein, Plotkin and Rao =-=[KPR93]-=- showed that planar graphs are O(1)-decomposable, and that more generally, graphs excluding a fixed minor of size r are O(r3 )decomposable. Fakcharoenphol and Talwar [FT03] improved the latter bound t... |

107 | Segmentation by grouping junctions. In: - Ishikawa, Geiger - 1998 |

96 | A constant-factor approximation algorithm for the multicommodity rent-or-buy problem
- Kumar, Gupta, et al.
- 2002
(Show Context)
Citation Context ...ime in the computer vision community. A polynomial-time algorithm for line metrics and a constant-factor approximation for uniform metrics were given by Boykov et al. [BVZ98, BVZ01]. Gupta and Tardos =-=[GT00]-=- gave a constant factor approximation on truncated line metrics. Kleinberg and Tardos [KT02] gave a 2-approximation algorithm for the case of a uniform metric on the labels, and combined this with Bar... |

88 | Approximating a finite metric by a small number of tree metrics. - Charikar, Chekuri, et al. - 1998 |

77 | Approximation algorithms for the metric labeling problem via a new linear programming formulation.
- CHEKURI, KHANNA, et al.
- 2001
(Show Context)
Citation Context ...rics. Fakcharoenphol et al. [FRT03] recently improved Bartal’s result, leading to an improved bound of O(log k). The earthmover LP was proposed independently by Charikar [Cha00] and by Chekuri et al=-=. [CKNZ01]-=-. The first successful use of this LP was in [CKNZ01], where it was used to give matching or improved algorithms for certain classes of distance functions d (convex and truncated linear), which had be... |

71 | An improved approximation algorithm for multiway cut.
- Calinescu, Karloff, et al.
- 2000
(Show Context)
Citation Context ...It is known that a simple randomized algorithm based on the semi-metric LP relaxation matches this factor, and that the integrality gap for this LP is also 2(1 − 1/k) [Vaz01, p.155]. Calinescu et al=-=. [CKR00]-=- strengthened the LP 3 Since several nodes may be mapped onto the same point in the containing metric, the induced distances between mapped nodes form only a semi-metric; hence the name. Our relaxatio... |

67 | Approximation algorithms for the 0-extension problem.
- CALINESCU, KARLOFF, et al.
- 2004
(Show Context)
Citation Context ...gram is integral when the terminal metric is a tree (actually, a larger class of bipartite graphs that contains trees; here, a tree metric cannot contain Steiner nodes). Calinescu, Karloff and Rabani =-=[CKR01]-=- gave an O(log k) approximation for 0-extension based on this LP relaxation. For the special case of input graphs that are planar, they gave an O(1) approximation algorithm. In fact, their algorithm e... |

60 | Low diameter graph decompositions, - Linial, Saks - 1993 |

50 | Rounding algorithms for a geometric embedding of minimum multiway cut. - Karger, Klein, et al. - 1999 |

46 |
Minimum 0-extensions of graph metrics
- Karzanov
- 1998
(Show Context)
Citation Context ...ound to O(r2 ). Charikar et al. [CCG + 98] showed that ℓ d p-metrics are d 1 1 max{ p ,1− p } - decomposable for any p ≥ 1, and that this bound is tight. The 0-extension problem was posed by Kar=-=zanov [Kar98]-=-, who gave an LP relaxation that we will call the semi-metric LP relaxation. He showed that this linear program is integral when the terminal metric is a tree (actually, a larger class of bipartite gr... |

33 | An improved approximation algorithm for the 0-extension problem
- Fakcharoenphol, Harrelson, et al.
- 2003
(Show Context)
Citation Context ...al case of input graphs that are planar, they gave an O(1) approximation algorithm. In fact, their algorithm extends to αdecomposable input graphs, giving an O(α) approximation. Fakcharoenphol et al=-=. [FHRT03] imp-=-roved the general result to O(log k/ log log k). On the other hand, the semi-metric relaxation is known to have an Ω( √ log k) integrality gap [CKR01]. Finally, we note that Lee and 2 A stronger d... |

33 | Steiner points in tree metrics don’t (really) help.
- Gupta
- 2001
(Show Context)
Citation Context ...m 3.1. (Fakcharoenphol et al. [FRT03]) For every n-point metric d there is a probabilistic tree approximation with distortion O(log n) from which we can sample in polynomial time. Theorem 3.2. (Gupta =-=[Gup01]) For every tree T =-=- (V ′ , E, w) and a set of required vertices V ⊆ V ′ , there exists a tree T ∗ = (V, E ∗ , w ∗ ) such that for all u, v ∈ V , dT (u, v) ≤ dT ∗(u, v) ≤ 8dT (u, v). Here is our algor... |

15 | Markov random with ecient approximations - Boykov, Veksler, et al. |

14 | Multicommodity max- min-cut theorems and their use in designing approximation algorithms - Leighton, Rao - 1999 |

10 | Approximation algorithms for classi problems with pairwise relationships: Metric labeling and markov random - Kleinberg, Tardos - 2000 |

7 | Markov random fields with e#cient approximations - Boykov, Veksler, et al. - 1998 |

5 |
Improved decompositions of graphs with forbidden minors
- Fakcharoenphol, Talwar
- 2003
(Show Context)
Citation Context ...le. Klein, Plotkin and Rao [KPR93] showed that planar graphs are O(1)-decomposable, and that more generally, graphs excluding a fixed minor of size r are O(r3 )decomposable. Fakcharoenphol and Talwar =-=[FT03] impro-=-ved the latter bound to O(r2 ). Charikar et al. [CCG + 98] showed that ℓ d p-metrics are d 1 1 max{ p ,1− p } - decomposable for any p ≥ 1, and that this bound is tight. The 0-extension problem ... |

5 | Ecient matching of pictorial structures - Felzenszwalb, Huttenlocher |

3 | Metric decomposition, smooth measures, and clustering - Lee, Naor - 2004 |