A monotone CNF formula is a Boolean formula in conjunctive normal form where each variable appears positively. We design a deterministic fully polynomial-time approximation scheme (FPTAS) for counting the number of satisfying assignments for a given monotone CNF formula when each variable appears in at most 5 clauses. Equivalently, this is also an FPTAS for counting set covers where each set co...

An edge cover of a graph is a set of edges in which each vertex has at least one of its incident edges. The problem of counting the number of edge covers is #P-complete and was shown to admit a fully polynomial-time approximation scheme (FPTAS) recently [10]. Counting weighted edge covers is the problem of computing the sum of the weights for all the edge covers, where the weight of each edge c...

Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system invo...

We investigate the problem of computing the strength of a graph. We describe in this article the first polyhedral formulation for the weighted strength in polynomial size of the problem, that isO(mn), where n is the number of vertices andm the number of edges. Moreover, we describe a surprisingly simple FPTAS that gives the strength within 1+ ǫ in time O(m log(n) log(mn )/ǫ ) and space O(m), ou...

The periodic resource model of Shin and Lee [18] provides a flexible, simple framework for designing compositional real-time systems. Each component in the periodic resource model has an interface which specifies the period and capacity of the resource used to schedule the component. Unfortunately, the best-known exact algorithms for determining the interface parameters for a components in the ...

We study a transportation problem where two heavy-duty trucks travel across the national highway from separate origins to destinations, subject individual deadline constraints. Our objective is minimize their total fuel consumption by jointly optimizing path planning, speed and platooning configuration. Such two-truck pervasive in practice yet challenging solve due hard constraints enormous con...