Matrix analysis
Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices
SIAM Journal on Control and Optimization
A primal-dual potential reduction method for problems involving matrix inequalities
Mathematical Programming: Series A and B
Efficient approximation algorithms for semidefinite programs arising from MAX CUT and COLORING
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Cone-LP's and Semidefinite Programs: Geometry
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Geometric Approach to Betweenness
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A 7/8-Approximation Algorithm for MAX 3SAT?
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Approximate graph coloring by semidefinite programming
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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The essential part of the best known approximation algorithm for graph MAXCUT is approximately solving MAXCUT's semidefinite relaxation. For a graph with n nodes and m edges, previous work on solving its semidefinite relaxation for MAXCUT requires space Õ(n2). Under the assumption of exact arithmetic, we show how an approximate solution can be found in space O(m + n1.5), where O(m) comes from the input; and therefore reduce the space required by the best known approximation algorithm for graph MAXCUT. Using the above space-efficient algorithm as a subroutine, we show an approximate solution for COLORING's semidefinite relaxation can be found in space O(m)+ Õ(n1.5). This reduces not only the space required by the best known approximation algorithm for graph COLORING, but also the space required by the only known polynomial-time algorithm for finding a maximum clique in a perfect graph.