Related papers: Approximation Algorithms for Complex-Valued Ising …
We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function, magnetizations, and correlations. The results…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions…
We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
In a recent breakthrough work, Gartland and Lokshtanov [FOCS 2020] showed a quasi-polynomial-time algorithm for Maximum Weight Independent Set in $P_t$-free graphs, that is, graphs excluding a fixed path as an induced subgraph. Their…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
Finding the ground state of an Ising-spin glass on general graphs belongs to the class of NP-hard problems, widely believed to have no efficient polynomial-time algorithms for solving them. An approach developed in computer science for…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…
The Marcus-Spielman-Srivastava theorem (Annals of Mathematics, 2015) for the Kadison-Singer conjecture implies the following result in spectral graph theory: For any undirected graph $G = (V,E)$ with a maximum edge effective resistance at…
The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…
One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This…
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three vertices into a tree. The polynomial time algorithm…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…