B. Chor, M. Sudan, "A geometric approach to betweenness," Proc. 3rd European Symposium on Algorithms, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the solution x i = sgn(hr; v i i) The expected value of this solution can be compared to the value of the relaxation, and this leads to randomized approximation algorithms. This technique has been applied, with modi cations, to several other problems in combinatorial optimization (e.g. [3, 4, 8, 9, 17, 22, 27, 30]) Almost any randomized approximation algorithm based on the hyperplane technique applied to a semide nite relaxation can be derandomized, as was shown by Mahajan and Ramesh [21] In the meantime, researchers in mathematical programming have shown that the interior point methods that extend ....

B. Chor and M. Sudan. A geometric approach to betweenness. SIAM Journal on Discrete Mathematics, 11:511-523, 1998.

....by modifying its solution before applying the random hyperplane technique. This leads to an improvement in the performance guarantee from 0:796 to 0:859 for MAXDICUT. More applications of semidefinite programming relaxations in the design of approximation algorithms can for instance be found in [22, 5, 9, 46]. We contribute to this line of research: The only problems in combinatorial optimization where the random hyperplane technique discussed above has proved useful in the design of approximation algorithms so far are maximization problems, see also [9, 46] The reason is that up to now only lower ....

B. Chor and M. Sudan. A geometric approach to betweenness. In P. Spirakis, editor, Algorithms -- ESA '95, volume 979 of Lecture Notes in Computer Science, pages 227 -- 237. Springer, Berlin, 1995.

....the solution x i = sgn(#r, v i #) The expected value of this solution can be compared to the value of the relaxation, and this leads to randomized # approximation algorithms. This technique has been applied, with modifications, to several other problems in combinatorial optimization (e.g. [3, 4, 8, 9, 17, 22, 27, 30]) Almost any randomized approximation algorithm based on the hyperplane technique applied to a semidefinite relaxation can be derandomized, as was shown by Mahajan and Ramesh [21] In the meantime, researchers in mathematical programming have shown that the interior point methods that extend ....

B. Chor and M. Sudan. A geometric approach to betweenness. SIAM Journal on Discrete Mathematics, 11:511--523, 1998.

....by modifying its solution before applying the random hyperplane technique. This leads to an improvement in the performance guarantee from 0#796 to 0#859 for MAXDICUT. More applications of semidefinite programming relaxations in the design of approximation algorithms can for instance be found in [25, 5, 11]. We contribute to this line of research: The only problems in combinatorial optimization where the random hyperplane technique discussed above has proved useful in the design of approximation algorithms so far are maximization problems. The reason is that up to now only lower bounds on the ....

B. Chor and M. Sudan. A geometric approach to betweenness. In P. Spirakis, editor, Algorithms -- ESA '95, volume 979 of Lecture Notes in Computer Science, pages 227 -- 237. Springer, Berlin, 1995.

....development of interior point algorithms [23, 32, 1, 37, 21, 25, 2, 33] practical methods for computing these relaxations became available. This encouraged research in the field and, as a consequence, several new approximation results based on semidefinite relaxations appeared within short time [14, 29, 13, 5, 12]. Most semidefinite relaxations can be improved in a canonical way by a cutting plane approach. Computational results show that the corresponding bounds are of high quality [19, 22, 20, 24, 40, 39] However, semidefinite relaxations are expensive to compute. In this paper we try to explore the ....

B. Chor and M. Sudan. A geometric approach to betweenness. In ESA '95 Proceedings, volume 979 of Lecture Notes in Computer Science, pages 227--237. Springer, 1995.

....r from the n dimensional normal distribution, and deriving the solution x i = sgn(hr; v i i) The expected value of this solution can be compared to the value of the relaxation. This technique has been applied, with modifications, to several other problems in combinatorial optimization (e.g. [2, 3, 6, 7, 12, 14, 21, 23]) In the meantime, researchers in mathematical programming have shown that the interior point methods that extend polynomial time solvability from linear programming to semidefinite programming also extend polynomial time solvability to the class of symmetric cones. This includes the second order ....

B. Chor and M. Sudan. A geometric approach to betweenness. SIAM Journal on Discrete Mathematics, 11:511--523, 1998.

....w 1 = v 1 and w i = 1 Gamma (v T 1 v i ) v i (v T 1 v i )v 1 , for some function (x) This has been used successfully, see [15, 46, 41] for example. The random hyperplane technique can also be used to obtain an ordering. So far, there has been only one such application, by Chor and Sudan [9] for the betweenness problem. In this case, we are given a ground set V and triplets (x i ; x j ; x k ) 2 V Theta V Theta V and we would like to find an ordering which maximizes the number of given triplets (x i ; x j ; x k ) for which x j is between x i and x k . In the case of satisfiable ....

B. CHOR and M. SUDAN. A geometric approach to betweenness. In Proc. of 3rd Europ. Symp. on Algs., volume LNCS 979 of Lecture Notes in Computer Science, pages 227--237,

....solution before applying the random hyperplane technique. This leads to an improvement in the performance guarantee from 0:796 to 0:859 for MaxDiCut. More applications of semide nite programming relaxations in the design of approximation algorithms can for instance be found in [Karger et al. 1998; Chor and Sudan 1998; Frieze and Jerrum 1997] We contribute to this line of research: The only problems in combinatorial optimization where the random hyperplane technique discussed above has proved useful in the design of approximation algorithms so far are maximization problems. The reason is that up to now only ....

Chor, B. and Sudan, M. 1998. A geometric approach to betweenness. SIAM Journal on Discrete Mathematics 11, 511 - 523.

....graph. Besides MAXCUT and COLORING, the technique of semidefinite programming has been successful in designing approximation algorithms for many other optimization problems, such as MAX DICUT [63, 51] MAX SAT [63, 51] MAX BISECTION [54] MAX k CUT [54] MAX STABLE SET [6] and BETWEENNESS [43]. Each of these improved algorithms is based on obtaining a near optimal solution to a semidefinite program, which is referred as the semidefinite relaxation of the underlining optimization problem. Therefore how to approximately solve these semidefinite relaxations efficiently, in both time and ....

....Their result is a major breakthrough in designing approximation algorithms in that for the first time they successfully adapt a nonlinear programming technique to design approximation algorithm. Much research, including the results described in this thesis, was prompted by their pioneering work [86, 55, 51, 43, 94, 95, 104, 78, 111, 6, 30, 88, 98]. There are also some results on approximation algorithms for MAXCUT on special graphs. It is known that MAXCUT has a polynomial time approximation scheme when the given graph is dense [49, 10] 2.2.2 COLORING COLORING [84] has applications in register allocation, time tabling, scheduling, ....

B. Chor and M. Sudan. A geometric approach to betweenness. In Proceedings of the Third Annual European Symposium Algorithms, pages 227-- 237, Corfu, Greece, 25--27 Sept. 1995. 103

.... 16] there are many probabilistic analyses of various approaches [15, 4, 28, 27, 26] and a wide variety of computational techniques have been employed or suggested, including greedy algorithms [18] simulated annealing [20, 25, 2, 1] linear programming [7, 12, 8] and semidefinite programming [6]. In this paper we develop a maximum likelihood approach for a type of physical mapping known as the samplingwithout replacement protocol. The protocol is inexpensive, simple to carry out in the lab, and uses widelyavailable technology. Organisms that have been mapped with this technique include ....

Chor, B. and M. Sudan. "A geometric approach to betweenness. " Proceedings of the European Symposium on Algorithms, Springer-Verlag Lecture Notes in Computer Science 979, 227--237, 1995.

.... section have been extended and generalized to other combinatorial optimization problems: the maximum dicut problem and the maximum 2 satisfiability problem [20,18] the problem of coloring 3colorable graphs [30] the maximum k cut and maximum bisection problems [19] and the betweenness problem [12]. 6 Embeddings of Finite Metric Spaces We would like to conclude with some open problems related to the power of semidefinite programming for the sparsest cut problem. This is a fascinating area but, unfortunately, we will be able to explore only the tip of the iceberg. We first collect some ....

B. Chor and M. Sudan. A geometric approach to betweenness. In Proc. of 3rd Europ. Symp. on Algs., volume LNCS 979 of Lecture Notes in Computer Science, pages 227--237, 1995.

....this work, Karger, Motwani, and Sudan [19] discovered the best known approximation algorithm for coloring a k colorable graph. Besides MAXCUT and COLORING, the technique of using semidefinite programming has been successful in designing approximation algorithms for many other optimization problems [4, 12, 9, 12, 9, 20, 11, 2, 7, 3]. Each of these improved algorithms is based on obtaining a near optimal solution to a semidefinite program, which is referred as the semidefinite relaxation of the underlining optimization problem. Therefore how to approximately solve these semidefinite relaxations efficiently, both in time and ....

B. Chor and M. Sudan. A geometric approach to betweenness. In Proceedings of the Third Annual European Symposium Algorithms, pages 227--237, 1995.

....in that we have both betweenness and nonbetweenness constraints, and we are optimizing a weighted sum of violations. Opatrny [Opa79] has shown that simply deciding whether a set of elements can be linearly ordered to satisfy a collection of betweenness constraints is NP complete. Chor and Sudan [CS95] present an approximation algorithm for the classical Betweenness Problem that either finds a feasible solution, or finds a linear order that satisfies at least one half of the constraints. They do not consider nonbetweenness constraints or weighted constraints. 2.1 Variables Our formulation of ....

B. Chor and M. Sudan. A geometric approach to betweenness. In P. Spirakis, editor, Algorithms -- ESA '95, volume 979 of Lecture Notes in Computer Science, pages 227--237. Springer, 1995.

....by modifying its solution before applying the random hyperplane technique. This leads to an improvement in the performance guarantee from 0:796 to 0:859 for MAXDICUT. More applications of semidefinite programming relaxations in the design of approximation algorithms can for instance be found in [26, 6, 12]. We contribute to this line of research: The only problems in combinatorial optimization where the random hyperplane technique discussed above has proved useful in the design of approximation algorithms so far are maximization problems. The reason is that up to now only lower bounds on the ....

B. Chor and M. Sudan. A geometric approach to betweenness. In P. Spirakis, editor, Algorithms -- ESA '95, volume 979 of Lecture Notes in Computer Science, pages 227 -- 237. Springer, Berlin, 1995.

.... from restriction fragment length data [18, 13] radiation hybrid mapping [4, 31] and optical mapping [26, 21, 29, 23] and a variety of computational techniques have been suggested, including simulated annealing [12, 25, 14, 33, 1, 2] linear programming [9, 17, 10] and semidefinite programming [7]. In this paper we study a new formulation of physical mapping by a procedure known as the sampling withoutreplacement protocol. The protocol is inexpensive, easy to perform, and has been used to map several organisms, including Schizosaccharomyces pombe [24] Aspergillus nidulans [30] and ....

Chor, B. and M. Sudan. "A geometric approach to betweenness. " Proceedings of the European Symposium on Algorithms, Springer-Verlag Lecture Notes in Computer Science 979, 227--237, 1995.

....of theoretic nature [12] A new rush of theoretical results in the early nineties [22, 6, 26] and the development of interior point algorithms for semidefinite programming [17, 24, 1, 28, 15, 19, 25] spurred interest for the field. Within short time several results in approximation theory [10, 23, 9, 5, 8] were published giving further evidence for the high quality of semidefinite programming bounds. Although a general framework for designing semidefinite relaxations of linear and quadratic 0 1 programming problems is available [22, 13, 16] only few papers presenting computational experience are ....

B. Chor and M. Sudan. A geometric approach to betweenness. In ESA '95 Proceedings, volume 979 of Lecture Notes in Computer Science, pages 227--237. Springer, 1995.

.... and optical mapping [20, 14, 16] there are many probabilistic analyses of various approaches [15, 4, 27, 26, 25] and a wide variety of computational techniques have been employed or suggested, including simulated annealing [19, 24, 2, 1] linear programming [7, 12] and semidefinite programming [6]. Extended abstract submitted to the 3rd ACM Conference on Computational Molecular Biology (RECOMB 99) y Corresponding author. Department of Computer Science, University of Georgia, Athens, GA 30602 7404. Email: kece cs.uga.edu. Research supported by a National Science Foundation CAREER ....

Chor, B. and M. Sudan. "A geometric approach to betweenness." Proceedings of the European Symposium on Algorithms, Springer-Verlag Lecture Notes in Computer Science 979, 227--237, 1995.

....to color a k colorable graph with O(n 1 Gamma 3 k 1 ) colors in polynomial time. Frieze and Jerrum [18] have used the technique to devise approximation algorithms for the maximum k way cut problem that improve on the previously best known 1 Gamma 1=k performance guarantee. Chor and Sudan [10] apply ideas from this paper to the betweeness problem. Thus it seems likely that the techniques in this paper will continue to prove useful in designing approximation algorithms. We expect that in practice the performance of our algorithms will be much better than the worst case bounds. We have ....

B. Chor and M. Sudan. A geometric approach to betweenness. In Proceedings of the European Symposium on Algorithms, 1995.

.... from restriction fragment length data [15, 11] radiation hybrid mapping [4, 25] and optical mapping [22, 17, 23, 19] and a variety of computational techniques have been suggested, including simulated annealing [10, 21, 12, 27, 1, 2] linear programming [8, 14, 9] and semidefinite programming [6]. In this paper we study a new formulation of physical mapping by a procedure known as the sampling without replacement protocol. The protocol is inexpensive, easy to perform, and has been used to map several organisms, including Schizosaccharomyces pombe [20] Aspergillus nidulans [24] and ....

Chor, B. and M. Sudan. "A geometric approach to betweenness." Proceedings of the European Symposium on Algorithms, Springer-Verlag Lecture Notes in Computer Science 979, 227--237, 1995.

....for laboratory error (Slonim 1996; Stein et al. 1997) RHMAPPER first produces a sparse framework map, containing a subset of the markers whose relative order is deduced with high certainty. The construction of the framework map uses a heuristic to solve the betweenness problem (Opatrny 1979; Chor and Sudan 1998). The rest of the markers are placed into bins relative to the framework markers to form a placement map. The package SAMMAPPER (Stewart et al. 1997) divides the markers to strongly linked groups and orders these groups. The optimization criteria is maximum likelihood. Simulated annealing is ....

Chor, B. and M. Sudan. 1998. A geometric approach to betweenness.

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B. Chor, M. Sudan, "A geometric approach to betweenness," Proc. 3rd European Symposium on Algorithms, 1995.

No context found.

B. Chor and M. Sudan. A geometric approach to betweenness. In P. Spirakis, editor, Algorithms -- ESA '95, volume 979 of Lecture Notes in Computer Science, pages 227--237. Springer, 1995.

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B. Chor and M. Sudan. A geometric approach to betweenness. In Proceedings of the European Symposium on Algorithms, 1995.

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B. Chor and M. Sudan. A geometric approach to betweenness. In Proceedings of the European Symposium on Algorithms, 1995.

No context found.

B. CHOR and M. SUDAN. A geometric approach to betweenness. In Proc. of 3rd Europ. Symp. on Algs., volume LNCS 979 of Lecture Notes in Computer Science, pages 227--237, 1995.

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