Graph coloring is arguably the most exhaustively studied problem in the area of approximate counting. It is conjectured that there is a fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for counting the number of proper colorings as long as q ≥ ∆ + 1, where q is the number of colors and ∆ is the maximum degree of the graph. The bound of q = ∆ + 1 is the uniqueness threshold ...

We present a fully polynomial time approximation scheme (FPTAS) for optimizing a very general class of nonlinear functions of low rank over a polytope. Our approximation scheme relies on constructing an approximate Pareto-optimal front of the linear functions which constitute the given low-rank function. In contrast to existing results in the literature, our approximation scheme does not requir...

We provide the first fully polynomial time approximation scheme (FPTAS) for computing an approximate mixedstrategy Nash equilibrium in graphical multi-hypermatrix games (GMhGs), which are generalizations of normal-form games, graphical games, graphical polymatrix games, and hypergraphical games. Computing an exact mixed-strategy Nash equilibria in graphical polymatrix games is PPADcomplete and ...

We address a variant of the classical knapsack problem in which an upper bound is imposed on the number of items that can be selected. This problem arises in the solution of real-life cutting stock problems by column generation, and may be used to separate cover inequalities with small support within cutting plane approaches to integer linear programs. We focus our attention on approximation al...

A basic problem in the quality-of-service (QoS) analysis of multiagent distributed systems is to find optimal routes for the mobile agents that incrementally fuse the data as they visit hosts in the distributed system. The system is modeled as a directed acyclic graph in which the nodes represent hosts and the edges represent links between them. Each edge is assigned a cost (or benefit) and wei...

We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a new technique for reducing the number of jobs while remaining close to the optimal solution. We also present an FPTAS for the classical machine covering proble...

Modern organizations (e.g., hospitals, social networks, government agencies) rely heavily on audit to detect and punish insiders who inappropriately access and disclose confidential information. Recent work on audit games models the strategic interaction between an auditor with a single audit resource and auditees as a Stackelberg game, augmenting associated well-studied security games with a c...

The Integer Knapsack Problem with Set-up Weights (IKPSW) is a generalization of the classical Integer Knapsack Problem (IKP), where each item type has a set-up weight that is added to the knapsack if any copies of the item type are in the knapsack solution. The k-item IKPSW (kIKPSW) is also considered, where a cardinality constraint imposes a value k on the total number of items in the knapsack...

We propose a computationally efficient Fully Polynomial-Time Approximation Scheme(FPTAS) to compute an approximation with arbitrary precision of the value function of convexstochastic dynamic programs, using the technique of K-approximation sets and functions introducedby Halman et al. (2009). This paper deals with the convex case only, and it has the following con-tributions: F...

The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous 0-1 Knapsack Problem (0-1 KP). In contrast to 0-1 KP, an arbitrary number of copies of every item can be taken in UKP. Since UKP is NP-hard, fully polynomial time approximation schemes (FPTAS) are of great interest. Such algorithms find a solution arbitrarily close to the optimum OPT(I), i.e. of value at least (1− ε)OPT(...