Related papers: FPTAS for #BIS with Degree Bounds on One Side
We are concerned with the problem of scheduling $n$ jobs onto $m$ identical machines. Each machine has to be in operation for a prescribed time, and the objective is to minimize the total machine working time. Precisely, let $c_i$ be the…
We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely $f$-Balanced Independent Set ($f$-BIS) and $f$-Balanced Dominating Set ($f$-BDS). Let $G=(V,E)$ be a vertex-colored interval…
Here we prove that counting maximum matchings in planar, bipartite graphs is #P-complete. This is somewhat surprising in the light that the number of perfect matchings in planar graphs can be computed in polynomial time. We also prove that…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
#NFA refers to the problem of counting the words of length $n$ accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical.…
We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling…
The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum weight sum. MWIS is one of the most investigated and most important algorithmic…
We study the complexity of approximating the independent set polynomial $Z_G(\lambda)$ of a graph $G$ with maximum degree $\Delta$ when the activity $\lambda$ is a complex number. This problem is already well understood when $\lambda$ is…
We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes. The threshold we obtain is almost tight up to an integrality gap. Our technique is based on…
Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core…
We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an…
When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy $F$, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An algorithm was recently…
In this paper we study the MAX-CUT problem on power law graphs (PLGs) with power law exponent $\beta$. We prove some new approximability results on that problem. In particular we show that there exist polynomial time approximation schemes…
We consider the computational problem of finding short paths in the skeleton of the perfect matching polytope of a bipartite graph. We prove that unless $P=NP$, there is no polynomial-time algorithm that computes a path of constant length…
In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of…
Given $n$ independent random variables $X_1, X_2, ..., X_n$ and an integer $C$, we study the fundamental problem of computing the probability that the sum $X=X_1+X_2+...+X_n$ is at most $C$. We assume that each random variable $X_i$ is…
We consider a natural, yet seemingly not much studied, extremal problem in bipartite graphs. A bi-hole of size $t$ in a bipartite graph $G$ is a copy of $K_{t, t}$ in the bipartite complement of $G$. Let $f(n, \Delta)$ be the largest $k$…
The problem of realizing a given degree sequence by a multigraph can be thought of as a relaxation of the classical degree realization problem (where the realizing graph is simple). This paper concerns the case where the realizing…
Given a non-deterministic finite automaton (NFA) A with m states, and a natural number n (presented in unary), the #NFA problem asks to determine the size of the set L(A_n) of words of length n accepted by A. While the corresponding…
The Maximum Weight Independent Set of Polygons problem is a fundamental problem in computational geometry. Given a set of weighted polygons in the 2-dimensional plane, the goal is to find a set of pairwise non-overlapping polygons with…