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On the Complexity of Dualization of Monotone Disjunctive Normal Forms
We show that the duality of a pair of monotone disjunctive normal forms of sizencan be tested inno(logn)time.
Rounding of Polytopes in the Real Number Model of Computation
- L. Khachiyan
- Mathematics, Computer Science
- Math. Oper. Res.
- 1 May 1996
It is shown that the problem of 1 + en-rounding of A can be solved in Om3.5 lnme-1 operations to a relative accuracy of e in the volume, and that bounds hold for the real number model of computation. Expand
Coordination Complexity of Parallel Price-Directive Decomposition
The coordination complexity of approximate price-directive decomposition PDD for the general block-angular convex resource sharing problem in K blocks and M nonnegative block-separable coupling constraints is studied and the fastest currently-known deterministic approximation algorithm for minimum-cost multicommodity flows is obtained. Expand
On the complexity of approximating the maximal inscribed ellipsoid for a polytope
We give a new polynomial bound on the complexity of approximating the maximal inscribed ellipsoid for a polytope.
A sublinear-time randomized approximation algorithm for matrix games
A parallel randomized algorithm which computes a pair of @e-optimal strategies for a given (m,n)-matrix game A achieves an almost quadratic expected speedup relative to any deterministic method. Expand
Approximate Max-Min Resource Sharing for Structured Concave Optimization
- M. Grigoriadis, L. Khachiyan, L. Porkolab, J. Villavicencio
- Mathematics, Computer Science
- SIAM J. Optim.
- 1 April 2000
We present a Lagrangian decomposition algorithm which uses logarithmic potential reduction to compute an $\varepsilon$-approximate solution of the general max-min resource sharing problem with M… Expand
On Generating the Irredundant Conjunctive and Disjunctive Normal Forms of Monotone Boolean Functions
It is shown that for some classes of polynomial-time computable monotone Boolean functions it is NP-hard to test either of the conditions D′=D or C′=C, which provides evidence that for each of these classes neither conjunctive nor disjunctive irredundant normal forms can be generated in total (or incremental) quasi-polynomial time. Expand
The polynomial solvability of convex quadratic programming
Abstract AN ACCURATE quadratic programming algorithm is constructed, in which the amount of work is bounded by a polynomial of the length of the recording of the problem in the binary number system.
Fast Approximation Schemes for Convex Programs with Many Blocks and Coupling Constraints
This paper presents block-coordinate descent algorithms for the approximate solution of large structured convex programming problems and shows that feasibility as well as min-mix resource-sharing problems for such constraints can be solved to a relative accuracy. Expand
On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction
- L. Khachiyan, E. Boros, +4 authors Jihui Zhao
- Computer Science, Mathematics
- Theory of Computing Systems
- 7 April 2008
It is shown that the short paths node-wise interdiction problem can be efficiently solved by an extension of Dijkstra’s algorithm and the same inapproximability bounds hold for undirected graphs and/or node elimination. Expand