Integer Programming: Optimization and Evaluation Are Equivalent

Link to conference publication published by Springer: http://dx.doi.org/10.1007/978-3-642-03367-4We show that if one can find the optimal value of an integer linear programming problem in polynomial time, then one can find an optimal solution in polynomial time. We also present a proper generalization to (general) integer programs and to local search problems of the well-known result that optimization and augmentation are equivalent for 0/1-integer programs. Among other things, our results imply that PLS-complete problems cannot have “near-exact” neighborhoods, unless PLS = P.United States. Office of Naval Research (ONR grant N00014-01208-1-0029

Construction of a river buffalo (Bubalus bubalis) whole-genome radiation hybrid panel and preliminary RH mapping of chromosomes 3 and 10

The buffalo (Bubalus bubalis) not only is a useful source of milk, it also provides meat and works as a natural source of labor and biogas. To establish a project for buffalo genome mapping a 5,000-rad whole genome radiation hybrid panel was constructed for river buffalo and used to build preliminary RH maps from two chromosomes (BBU 3 and BBU10). The preliminary maps contain 66 markers, including coding genes, cattle ESTs and microsatellite loci. The RH maps presented here are the starting point for mapping additional loci, in particular, genes and expressed sequence tags that will allow detailed comparative maps between buffalo, cattle and other species to be constructed. A large quantity of DNA has been prepared from the cell lines forming the RH panel reported here and will be made publicly available to the international community both for the study of chromosome evolution and for the improvement of traits important to the role of buffalo in animal agriculture

On strong equilibria in the max cut game

Abstract. This paper deals with two games defined upon well known generalizations of max cut. We study the existence of a strong equilibrium which is a refinement of the Nash equilibrium. Bounds on the price of anarchy for Nash equilibria and strong equilibria are also given. In particular, we show that the max cut game always admits a strong equilibrium and the strong price of anarchy is 2/3.

Nash dynamics in constant player and bounded jump congestion games

Abstract. We study the convergence time of Nash dynamics in two classes of congestion games – constant player congestion games and bounded jump congestion games. It was shown by Ackermann and Skopalik [2] that even 3-player congestion games are PLS-complete. We design an FPTAS for congestion games with constant number of players. In particular, for any ɛ> 0, we establish a stronger result, namely, any sequence of (1 + ɛ)-greedy improvement steps converges to a (1 + ɛ)-approximate equilibrium in a number of steps that is polynomial in ɛ −1 and the size of the input. As the number of strategies of a player can be exponential in the size of the input, our FPTAS result assumes that a (1 + ɛ)-greedy improvement step, if it exists, can be computed in polynomial time. This assumption holds in previously studied models of congestion games, including network congestion games [9] and restricted network congestion games [2]. For bounded jump games, where jumps in the delay functions of resources are bounded by β, we show that there exists a game with an exponentially long sequence of α-greedy best response steps that does not converge to an α-approximate equilibrium, for all α ≤ β o(n / log n) , where n is the number of players and the size of the game is O(n). So in the worst case, Nash dynamics may fail to converge in polynomial time to such an approximate equilibrium. We also prove the same result for bounded jump network congestion games. In contrast, we observe that it is easy to show that a β 2n-approximate equilibrium is reached in at most n best response steps.