Finding Nash equilibrium in a two-player normal form game (2-Nash) is one of the most extensively studied problem within mathematical economics as well as theoretical computer science. Such a game can be represented by two payoff matrices A and B, one for each player. 2Nash is PPAD-complete in general, while in case of zero-sum games (B = −A) the problem reduces to LP and hence is in P. Extendi...

By implementing algorithmic versions of Sapozhenko's graph container methods, we give new algorithms for approximating the number independent sets in bipartite graphs. Our first algorithm applies to d $$ -regular, graphs satisfying a weak expansion condition: when is constant, and Ω ( log 2 / ) \Omega \left({\log}^2d/d\right) -expander, obtain an FPTAS sets. Previously such result > 5 d>5 was k...

We study the problem of approximating value matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in complex plane. When is a positive real, Jerrum and Sinclair showed that admits an FPRAS general graphs. For Patel Regts, building methods developed by Barvinok, FPTAS maximum degree Δ as long not negative real number less than or equal to −1/(4(Δ −1)). Our first mai...

Traditional studies of combinatorial auctions often only consider linear constraints (by which the demands for certain goods are limited by the corresponding supplies). The rise of smart grid presents a new class of auctions, characterized by quadratic constraints. Yu and Chau [AAMAS 13’] introduced the complex-demand knapsack problem, in which the demands are complex-valued and the capacity of...

The bootstrap is a nonparametric approach for calculating quantities, such as confidence intervals, directly from data. Since calculating exact bootstrap quantities is believed to be intractable, randomized resampling algorithms are traditionally used. Motivated by the fact that the variability from randomization can lead to inaccurate outputs, we propose a deterministic approach. First, we est...

In a standard f -connectivity network design problem, we are given an undirected graph G = (V,E), a cut-requirement function f : 2 → N, and non-negative costs c(e) for all e ∈ E. We are then asked to find a minimum-cost vector x ∈ N such that x(δ(S)) ≥ f(S) for all S ⊆ V . We focus on the class of such problems where f is a proper function. This encodes many well-studied NP-hard problems such a...

We consider sporadic tasks with static priorities and constrained deadlines to be executed upon a uniprocessor platform. Pseudo-polynomial time algorithms are known for computing worst-case response times for this task model. Some applications require to evaluate efficiently upper bounds of response times. For this purpose, we propose parametric algorithms that allow to make a tradeoff between ...

In this paper we study the Multiple Strip Packing (MSP) problem, a generalization of the well-known Strip Packing problem. For a given set of rectangles, r1, . . . , rn, with heights and widths ≤ 1, the goal is to find a non-overlapping orthogonal packing without rotations into k ∈ N strips [0, 1]× [0,∞), minimizing the maximum of the heights. We present an approximation algorithm with absolute...

In this paper we consider a generalization of the classical knapsack problem. While in the standard setting a fixed capacity may not be exceeded by the weight of the chosen items, we replace this hard constraint by a weight-dependent cost function. The objective is to maximize the total profit of the chosen items minus the cost induced by their total weight. We study two natural classes of cost...