Related papers: Fractionally Log-Concave and Sector-Stable Polynom…
The even discrete torus is the graph T_{L,d} on vertex set {0,...,L-1}^d (L even) with two vertices adjacent if they differ by 1 (mod L) on one coordinate. The hard-core measure with activity x on T_{L,d} is the distribution pi_x on the…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge…
We investigate structural properties of the cone of roots of relative Steiner polynomials of convex bodies. We prove that they are closed, monotonous with respect to the dimension, and that they cover the whole upper half-plane, except the…
Jerrum, Sinclair and Vigoda (2004) showed that the permanent of any square matrix can be estimated in polynomial time. This computation can be viewed as approximating the partition function of edge-weighted matchings in a bipartite graph.…
We formulate conditions on a set of log-concave sequences, under which any linear combination of those sequences is log-concave, and further, of conditions under which linear combinations of log-concave sequences that have been transformed…
We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, we show how to build a Steiner forest spanner for such graphs.…
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say $G$.…
\emph{Sampling} constitutes an important tool in a variety of areas: from machine learning and combinatorial optimization to computational physics and biology. A central class of sampling algorithms is the \emph{Markov Chain Monte Carlo}…
Given a graph $G$ with a terminal set $R \subseteq V(G)$, the Steiner tree problem (STREE) asks for a set $S\subseteq V(G) \setminus R$ such that the graph induced on $S\cup R$ is connected. A split graph is a graph which can be partitioned…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
Is perfect matching in NC? That is, is there a deterministic fast parallel algorithm for it? This has been an outstanding open question in theoretical computer science for over three decades, ever since the discovery of RNC matching…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise…
We provide some conditions for the graph of a Hoelder-continuous function on \bar{D}, where \bar{D} is a closed disc in the complex plane, to be polynomially convex. Almost all sufficient conditions known to date --- provided the function…
Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential…
We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edges are…