D. Karger, R. Motwani and M. Sudan, "Approximate graph coloring by semidefinite programming," Proc. 35th IEEE Symposium on Foundations of Computer Science, 1994, pp. 2--13.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....sets) in perfect graphs [16] This paper describes another such application. Spectral methods are closely related to the more general method of semidefinite programming, which has been applied successfully to many combinatorial problems (e.g. MAX CUT and MAX 2SAT [14] and graph coloring [18]) See Alizadeh [1] for a survey of semidefinite programming with applications to combinatorial optimization. Our result is important for several reasons. First, it provides new insight into the well studied C1P. Second, some important practical problems like envelope reduction for matrices and ....

D. Karger, R. Motwani, and M. Sudan, Approximate graph coloring by semidefinite programming, in Proc. 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 2--13.

....site the old and new labels have the same image under Psi. This can be seen by induction working in from distance k Gamma 1. It follows that Hom(T d ; H) is cold. 9 The methods used in the above proof call to mind the vector chromatic number of a graph H, defined by Karger, Motwani and Sudan [8] as the minimum k such that there exists a labeling Psi of V (H) by unit vectors in R jV (H)j in which adjacent nodes u and v satisfy h Psi(u) Psi(v)i Gamma k Gamma1 . Karger, Motwani and Sudan show that the vector chromatic number of H can be approximated arbitrarily closely in ....

D. Karger, R. Motwani and M. Sudan, Approximate graph coloring by semidefinite programming, J. ACM 45 (1998), 246--265.

....Blvd, Milpitas, CA 95035, msanjeev lsil.com, Fax: 408 433 8989 Indian Institute of Science, Bangalore, India, 560012, ramesh csa.iisc.ernet.in, Fax: 91 80344 1683. Karger, Motwani and Sudan obtained an algorithm for coloring any k colorable graph with O(n 1 Gamma3= k 1) log n) colors[12]; in particular, for 3 colorable graphs, this algorithm requires O(n :25 log n) colors. This improves upon the deterministic algorithm of Blum[3] which requires O(n 1 Gamma k Gamma4=3 8 5 n) colors for k colorable graphs. Frieze and Jerrum[7] obtained a .65 approximation algorithm for ....

....according to the density function jrj Gammar . It is not clear how P r(sign(v )jfl) can be computed for this distribution of . The Karger Motwani Sudan Coloring Algorithm. Our description of this algorithm is based on the conference proceedings version of their paper [12]. The Karger, Motwani, Sudan algorithm shows how to color a 3 colorable graph of n vertices with O(n log n) colors. The authors use a semidefinite program to obtain a set of vertex vectors such that v Delta w Gamma 2 , for all edges (v; w) Note that if these vectors are somehow constrained ....

[Article contains additional citation context not shown here]

D. Karger, R. Motwani and M. Sudan, Approximate Graph Coloring by Semidefinite Programming, 35th IEEE Symposium on Foundations of Computer Science, pp. 1--10, 1994.

....time such that the fraction of defect edges (with endpoints of the same colour) is provably small. The best known approximation was obtained by Frieze and Jerrum [9] using a semidefinite programming (SDP) relaxation which is related to the Lovasz # function. In a related work, Karger et al. [18] devised approximation algorithms for colouring k colourable graphs exactly in polynomial time with as few colours as possible. They also used an SDP relaxation related to the # function. In this paper we further explore semidefinite programming relaxations where graph colouring is viewed as a ....

....of k. For example, if k = 3 we can improve their bound from 0.832718 to 0.836008, and for k = 4 from 0.850301 to 0.857487. We also give a new asymptotic analysis of the Frieze Jerrum rounding scheme, that provides a unifying proof of the main results of both Frieze and Jerrum [9] and Karger et al. [18] for k 0. Keywords: Graph colouring, approximation algorithms, satisfiability, semidefinite programming, Lovasz # function, MAX k CUT 1 Introduction The Lovasz # function [23] of a graph G = V, E) forms the base for many semidefinite programming (SDP) relaxations of combinatorial ....

[Article contains additional citation context not shown here]

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. J. ACM, 45(2):246--265, 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 ....

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. In Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, pages 2 -- 13, 1994.

....in the design of a number of other approximation algorithms, for example the max k cut (Frieze and Jerrum [F J] a 0.931approximation algorithm for MAX 2 SAT (Feige and Goemans [F G] a 0. 859 approximation algorithm for MAX DICUT [F G] and approximate coloring (Karger, Motwani, and Sudan [K M S]) 5 Random walks on graphs Isoperimetric properties and eigenvalues treated in previous sections are closely related to the convergence rates of Markov chains. Several important randomized algorithms discovered in the last decade increased applicability of random walks and Markov chains in ....

D. Karger, R. Motwani, M. Sudan, Approximate graph coloring by semidefinite programming, Proc. 35th Ann. Symp. FOCS, 1994, pp. 2--13.

.... rounding them into values in f Gamma1; 1g; this is also the only probabilistic step in their algorithm. Over a year later at FOCS 95, S. Mahajan and Ramesh [MR95a] showed how to derandomize the rounding step in [GW94] as well as in the application of SDP for graph coloring, due to [KMS94] The proof of [MR95a] is technically quite tedious, and involves the evaluation of non trivial integrals. The main message of this paper is that with the right viewpoint derandomizations for the SDP rounding steps, and numerous similar algorithms, could have been achieved almost ....

....algorithms. Section 3 discusses the discrepancy problem (cf. Rag88] Section 4 discusses the derandomization of the randomized rounding step of the Goemans Williamson approximation algorithm for the MAX CUT problem [GW94] we omit details of the rounding algorithm for the coloring problem [KMS94] we do this to avoid testing the reader s patience once the point is made about how Nisan s work fits in these contexts, the rest is fairly easy) Section 5 presents a derandomization of the famous Johnson Lindenstrauss lemma, a result that has been making several appearances in the design of ....

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. In Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, pages 2--13, 1994.

.... polygon guarding problems [Hof96] load balancing [Jos95] wireless spectrum estimation [Kha98] circuit clustering [Sin99] and multi layer planar routing [Con93] Optimization algorithms for graph coloring may be classified into three major classes: exact [Bre79, Cou97] heuristic constructive [Kar98, Hal93, Lei79] and iterative (1) improvement [Cha87, Mor86, Veg99] In addition several specialized hardware platforms for efficient graph coloring has been developed including, ones based on couplet oscillators [Wu98] and reconfigurable FPGAs [Lee98] Fig. 3. Generic Non Greedy Probabilistic Iterative ....

D. Karger, R. Motwani, M. Sudan. Approximate graph coloring by semi-definite programming. Journal of the ACM, Vol. 45, No. 2, pp.246-65, 1998.

No context found.

D. Karger, R. Motwani and M. Sudan. Approximate graph coloring by semidefinite programming. Proceedings of the Thirty Fifth Annual Symposium on the Foundations of Computer Science, IEEE, 1994.

No context found.

D. Karger, R. Motwani and M. Sudan. Approximate graph coloring by semidefinite programming. Proceedings of the Thirty Fifth Annual Symposium on the Foundations of Computer Science, IEEE, 1994.

No context found.

D. Karger, R. Motwani and M. Sudan. Approximate graph coloring by semidefinite programming. Proceedings of the Thirty Fifth Annual Symposium on the Foundations of Computer Science, IEEE, 1994.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 2--13, 1994.

No context found.

D. Karger, R. Motwani and M. Sudan. Approximate graph coloring by semidefinite programming. Proceedings of the Thirty Fifth Annual Symposium on the Foundations of Computer Science, IEEE, 1994.

.... for such weak approximation algorithms was suggested by Blum [Bl] He showed that a polynomial time N factor approximation algorithm for Max Clique implies a polynomial time algorithm to color a three colorable graph with O(log N) colors [Bl] which is much better than currently known [KMS]. But perhaps N is the best possible. Resolving the approximation complexity of this basic problem seems, in any case, to be worth some effort. Gaps in clique size. Hardness of approximation (say of Max Clique) is typically shown via the construction of promise problems with gaps in max clique ....

D. Karger, R. Motwani and M. Sudan. Approximate graph coloring by semidefinite programming. Proceedings of the 35th Symposium on Foundations of Computer Science, IEEE, 1994, pp. 2--13.

No context found.

D. Karger, R. Motwani and M. Sudan, "Approximate graph coloring by semidefinite programming," Proc. 35th IEEE Symposium on Foundations of Computer Science, 1994, pp. 2--13.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 2--13, 1994.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. J. ACM, 45(2):246--265, 1998.

No context found.

D. Karger, R. Motwani, and M. Sudan (1994), "Approximate graph coloring by semidefinite programming", Proc. of the 35th IEEE Symposium on Foundations of Computer Science, pp. 2--13.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. J. ACM, 45(2):246--265, 1998.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. JACM, 45(2):246--265, 1998.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pages 2--13, 1994.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. Technical report, Department of Computer Science, Stanford University, 1994.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. JACM, 45(2):246--265, 1998.

No context found.

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. Journal of ACM, 45(2):246--265, 1998.

No context found.

D. KARGER, R. MOTWANI, and M. SUDAN. Approximate graph coloring by semidefinite programming. J. Assoc. Comput. Mach., 45:246--265, 1998.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC