Related papers: Approximate counting and sampling via local centra…
We determine the computational complexity of approximately counting and sampling independent sets of a given size in bounded-degree graphs. That is, we identify a critical density $\alpha_c(\Delta)$ and provide (i) for $\alpha <…
We study the problem of approximately counting matchings in hypergraphs of bounded maximum degree and maximum size of hyperedges. With an activity parameter $\lambda$, each matching $M$ is assigned a weight $\lambda^{|M|}$. The counting…
We give a deterministic polynomial-time approximation scheme (FPTAS) for the volume of the truncated fractional matching polytope for graphs of maximum degree $\Delta$, where the truncation is by restricting each variable to the interval…
We propose a deterministic algorithm for approximately counting the number of list colorings of a graph. Under the assumption that the graph is triangle free, the size of every list is at least $\alpha \Delta$, where $\alpha$ is an…
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…
We give an FPTAS for approximating the partition function of the hard-core model for bipartite graphs when there is sufficient imbalance in the degrees or fugacities between the sides $(L,R)$ of the bipartition. This includes, among others,…
We study the computational complexity of approximately counting the number of independent sets of a graph with maximum degree Delta. More generally, for an input graph G=(V,E) and an activity lambda>0, we are interested in the quantity…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
We propose an efficient $\epsilon$-differentially private algorithm, that given a simple {\em weighted} $n$-vertex, $m$-edge graph $G$ with a \emph{maximum unweighted} degree $\Delta(G) \leq n-1$, outputs a synthetic graph which…
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.…
It is shown in this note that approximating the number of independent sets in a $k$-uniform linear hypergraph with maximum degree at most $\Delta$ is NP-hard if $\Delta\geq 5\cdot 2^{k-1}+1$. This confirms that for the relevant sampling and…
We prove that given any $\alpha$-approximation LOCAL algorithm for Minimum Dominating Set (MDS) on planar graphs, we can construct an $f(g)$-round $(3\alpha+1)$-approximation LOCAL algorithm for MDS on graphs embeddable in a given Euler…
We prove that, unless P=NP, there is no polynomial-time algorithm to approximate within some multiplicative constant the average size of an independent set in graphs of maximum degree 6. This is a special case of a more general result for…
We study the \textsc{$\alpha$-Fixed Cardinality Graph Partitioning ($\alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two…
We show for a broad class of counting problems, correlation decay (strong spatial mixing) implies FPTAS on planar graphs. The framework for the counting problems considered by us is the Holant problems with arbitrary constant-size domain…
We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the…
We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on…