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; efficient… Expand

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 the… Expand

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

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

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

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 search… Expand

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

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

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 measure… Expand

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