We consider the approximation of two NP-hard problems: Minkowski Decomposition (MinkDecomp) of integral lattice polygons, and the related Multidimensional Subset Sum (kD-SS). We prove, through a gap-preserving reduction, that, for general dimension k, kD-SS does not have an FPTAS. For 2D-SS, we present an O(n/ ) approximation algorithm, where n is the set cardinality and bounds the approximatio...

We study a model that incorporates a budget constraint in a decision making problem. Our goal is to maximize the expected wealth, where in each time period we can either stop the business getting our current wealth or to continue one additional time period and getting a random revenue. We show that when the wealth is scalar, the problem is NP-hard and we provide an FPTAS. However, when the weal...

We show that finding a global optimal solution for the regularized Lq-minimization problem (q ≥ 1) is strongly NP-hard if the penalty function is concave but not linear in a neighborhood of zero and satisfies a very mild technical condition. This implies that it is impossible to have a fully polynomial-time approximation scheme (FPTAS) for such problems unless P = NP. This result clarifies the ...

We address the combined scheduling problem of maximizing the total reward of fixed-priority hard real-time systems with a given energy budget. We present a fully polynomial time approximation scheme (FPTAS) for the off-line job-level scheduling problem and an efficient heuristic for the task-level scheduling problem. We also describe an online algorithm which is effective in leveraging the exec...

We consider the parallel-machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the total completion time. We give a fully polynomial-time approximation scheme (FPTAS) for the case with m identical machines, where m is fixed. This study solves an open problem that has been posed in the literature...

Two-state spin systems is a classical topic in statistical physics. We consider the problem of computing the partition function of the systems on a bounded degree graph. Based on the self-avoiding tree, we prove the systems exhibits strong correlation decay under the condition that the absolute value of “inverse temperature” is small. Due to strong correlation decay property, an FPTAS for the p...

This paper addresses the problem of identifying a profit-maximizing schedule for jobs in just-in-time production line, where decision maker can adjust each job’s processing time, and thereby its quality level profit that be gained from it. The system comprises two sequential machines with transition period between them setup time after completion job on second machine. We first construct an exa...

Recently, there has been a wide spread of battery-operated embedded computing systems such as mobile and portable devices. For such systems, energy consumption is one of the most important design constraints because the battery operation time is a primary performance measure. Voltage scheduling, which adjusts the processor speed along with the supply voltage dynamically, is an effective techniq...