Related papers: Approximation Algorithms for Complex-Valued Ising …
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…
Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
We construct a deterministic approximation algorithm for computing a permanent of a $0,1$ $n$ by $n$ matrix to within a multiplicative factor $(1+\epsilon)^n$, for arbitrary $\epsilon>0$. When the graph underlying the matrix is a constant…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
Normalization of polynomials plays a vital role in the approximate basis computation of vanishing ideals. Coefficient normalization, which normalizes a polynomial with its coefficient norm, is the most common method in computer algebra.…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive…
Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…
We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a…
We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We give a comprehensive study of bin packing with conflicts (BPC). The input is a set $I$ of items, sizes $s:I \rightarrow [0,1]$, and a conflict graph $G = (I,E)$. The goal is to find a partition of $I$ into a minimum number of independent…
We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…