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Combinatorial Optimization: Algorithms and Complexity
This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficientExpand
Worst-case equilibria
In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of theExpand
Computational complexity
TLDR
Computational complexity is the realm of mathematical models and techniques for establishing impossibility proofs for proving formally that there can be no algorithm for the given problem which runs faster than the current one. Expand
Optimization, Approximation, and Complexity Classes
TLDR
It follows that such a complete problem has a polynomial-time approximation scheme iff the whole class does, and that a number of common optimization problems are complete for MAX SNP under a kind of careful transformation that preserves approximability. Expand
The Complexity of Markov Decision Processes
TLDR
All three variants of the classical problem of optimal policy computation in Markov decision processes, finite horizon, infinite horizon discounted, and infinite horizon average cost are shown to be complete for P, and therefore most likely cannot be solved by highly parallel algorithms. Expand
On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence
We define several new complexity classes of search problems, ''between'' the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of searchExpand
The Complexity of Multiterminal Cuts
TLDR
It is shown that the problem becomes NP-hard as soon as $k=3$, but can be solved in polynomial time for planar graphs for any fixed $k$, if the planar problem is NP- hard, however, if £k$ is not fixed. Expand
The Discrete Geodesic Problem
TLDR
An algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface and generalizes to the case of multiple source points to build the Voronoi diagram on the surface. Expand
Worst-case Equilibria
In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measureExpand
On a network creation game
TLDR
The Nash equilibria of this game are studied, and results suggesting that the "price of anarchy" in this context (the relative cost of the lack of coordination) may be modest are proved. Expand
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