We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour [10]. They presented an FPTAS for computing an approximate equilibrium, and conjectured that there is a polynomial algorithm for finding an exact equilibrium [9]. We extend their study in two directions: (1) We show that finding an exact equilibrium, even for two-player z...

Abstract Single-machine scheduling where jobs have a penalty for being late or rejected altogether is an important (sub)problem in manufacturing, logistics, and satellite scheduling. It known to be NP-hard the strong sense, there no polynomial-time algorithm that can guarantee constant-factor approximation (unless P=NP). We provide exact fixed-parameter tractable slack maximum number of time wi...

In this paper we propose a Fully Polynomial Time Approximation Scheme (FPTAS) for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of linear ratio functions. The class includes the well known ones of Linear (Sum-of-Ratios) Fractional Programming and Multiplicative Programming.

A new fully polynomial approximation scheme (FPTAS) is presented for the classical 0{1 knapsack problem. It considerably improves the space requirements. The two best previously known approaches need O(n+1=" 3) and O(n1=") space, respectively. Our new approximation scheme requires only O(n + 1=" 2) space while also reducing the running time.

Traditional incentive-compatible auctions for selling multiple goods to unconstrained and budgeted bidders can discriminate between bidders by selling identical goods at different prices. For this reason, A recent study by Feldman et al. dropped incentive compatibility and turned the attention to revenue maximizing envy-free item-pricing allocations for budgeted bidders. Envy-free allocations w...

In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS). 1998 ACM Subject Classification F.2.2

We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour [10]. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial algorithm for finding an exact equilibrium [9]. We extend their study in two directions: (1) We show that finding an exact equilibrium, even for two-player ...

Abstract In a widely-studied class of multi-parametric optimization problems, the objective value each solution is an affine function real-valued parameters. Then, goal to provide optimal set, i.e., set containing for non-parametric problem obtained by fixing parameter vector. For many however, minimum cardinality can contain super-polynomially solutions. Consequently, no polynomial-time exact ...