A special class of quadratic pseudo-boolean functions called “half-products” (HP) has recently been introduced. It has been shown that HP minimization, while NP-hard, admits a fully polynomial time approximation scheme (FPTAS). In this note, we provide a more efficient FPTAS. We further show how an FPTAS can also be derived for the general case where the HP function is augmented by a problem-de...

We design deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function for a class of multi-spin systems, extending the known approximable regime by an exponential scale. As a consequence, we have an FPTAS for the Potts models with inverse temperature β up to a critical threshold |β| = O( 1 ∆ ) where ∆ is the maximum degree, confirming a conjecture in [1...

For five single machine total tardiness problems a fully polynomial-time approximation scheme (FPTAS) based on a graphical algorithm is presented. The FPTAS has the best running time among the known approximation schemes for these problems.

We study the K -item knapsack problem ( i.e. , 1.5-dimensional problem), a generalization of famous 0–1 1-dimensional problem) in which an upper bound is imposed on number items selected. This fundamental importance and known to have broad range applications various fields. It well that, there no fully polynomial time approximation scheme (FPTAS) for d -dimensional when ? 2 unless P = NP. While...

An edge cover of a graph is a set of edges such that every vertex has at least an adjacent edge in it. We design a very simple deterministic fully polynomial-time approximation scheme (FPTAS) for counting the number of edge covers for any graph. Previously, approximation algorithm is only known for 3 regular graphs and it is randomized. Our main technique is correlation decay, which is a powerf...

Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm [5] and play an important role in the dichotomy of exact counting for Holant and CSP frameworks [6]. We generalize them to weighted cases and allow each vertex function to have different parameters, which is a much boarder family and #P-hard for exactly counting. We design a fully pol...

This paper addresses the Tardy/Lost penalty minimization with common due dates on a single machine. According to this performance measure, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Initially, we present a 2-approximation algorithm and examine its worst case ratio bound. Then, a pseudo-polynomial dynamic programming algorithm is de...

We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on infinite regular trees. This condition is of physical significance and is believed to be the right boundary between approximable and inapproximable. The FPTA...

In this paper, we investigate the parametric knapsack problem, in which the item profits are affine functions depending on a real-valued parameter. The aim is to provide a solution for all values of the parameter. It is well-known that any exact algorithm for the problemmay need to output an exponential number of knapsack solutions. We present a fully polynomial-time approximation scheme (FPTAS...