Essays in Game Theory
In Honor of Michael Maschler
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%P
24 Result(s)
within
Nimrod Megiddo
Mathematics
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Article
A modified layered-step interior-point algorithm for linear programming
The layered-step interior-point algorithm was introduced by Vavasis and Ye. The algorithm accelerates the path following interior-point algorithm and its arithmetic complexity depends only on the coefficient m...
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Article
New algorithms for generalized network flows
This paper, of which a preliminary version appeared in ISTCS'92, is concerned with generalized network flow problems. In a generalized network, each edgee = (u, v) has a positive ‘flow multiplier’a ...
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Book
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Chapter
On Probabilistic Machines, Bounded Rationality and Average-Case Complexity
The analogs of pure, mixed and behavior strategies in the context of algorithms are studied. It is shown that probabilistic machines are more powerful than probability distributions over deterministic ones, th...
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Article
A primal—dual infeasible-interior-point algorithm for linear programming
As in many primal—dual interior-point algorithms, a primal—dual infeasible-interior-point algorithm chooses a new point along the Newton direction towards a point on the central trajectory, but it does not con...
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Article
Theoretical convergence of large-step primal—dual interior point algorithms for linear programming
This paper proposes two sets of rules, Rule G and Rule P, for controlling step lengths in a generic primal—dual interior point method for solving the linear programming problem in standard form and its dual. T...
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Article
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality
The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NP-complete, even when all variables are binary. This paper deals with integer li...
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Chapter
A General NP-Completeness Theorem
Blum, Shub, and Smale [2] formalized a model of computation over a general ring. They proved an analogue of Cook’s theorem [3] over the reals. Smale [4] has recently raised the question of existence of NP-comp...
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Article
An interior point potential reduction algorithm for the linear complementarity problem
The linear complementarity problem (LCP) can be viewed as the problem of minimizingx T y subject toy=Mx+q andx, y⩾0. We are interested in finding a point withx T y <ε for a givenε > 0. The algorithm proceeds by i...
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Book
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Article
On the ball spanned by balls
The procedure for linear programming in linear time in fixed dimension is extended to solve in linear time certain nonlinear problems. Examples are the problem of finding the smallest ball enclosingn given balls,...
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Book
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Chapter
Pathways to the Optimal Set in Linear Programming
This chapter presents continuous paths leading to the set of optimal solutions of a linear programming problem. These paths are derived from the weighted logarithmic barrier function. The defining equations ar...
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Article
On the complexity of polyhedral separability
It is NP-complete to recognize whether two sets of points in general space can be separated by two hyperplanes. It is NP-complete to recognize whether two sets of points in the plane can be separated withk lines....
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Article
A note on degeneracy in linear programming
We show that the problem of exiting a degenerate vertex is as hard as the general linear programming problem. More precisely, every linear programming problem can easily be reduced to one where the second best...
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Article
Computing circular separability
Two sets of planar pointsS 1 andS 2 are circularly separable if there is a circle that enclosesS 1 but excludesS 2. We show that deciding whether two sets are circularly separable can be accomplished inO(n) time ...
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Article
On the expected number of linear complementarity cones intersected by random and semi-random rays
Lemke's algorithm for the linear complementarity problem follows a ray which leads from a certain fixed point (traditionally, the point (1,⋯, 1)T) to the point given in the problem. The problem also induces a set...
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Article
Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm
In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. C...
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Chapter
On the parametric nonlinear complementarity problem
A parametrized version of the nonlinear complementarity problem is formulated. The existence of a continuation of a solution is investigated and sufficient and necessary conditions for the monotonicity of such...
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Article
A monotone complementarity problem with feasible solutions but no complementary solutions
