Related papers: Deterministic polynomial-time approximation algori…
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…
Let $H$ be a $k$-graph on $n$ vertices, with minimum codegree at least $n/k + cn$ for some fixed $c > 0$. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in $H$ or a certificate that none exists.…
The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Neto\v{c}n\'y and Redig and the cluster expansion approach…
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…
Given a graph $G=(V, E)$ and and a proper labeling $f$ from $V$ to $\{1, ..., n\}$, we define $B(f)$ as the maximum absolute difference between $f(u)$ and $f(v)$ where $(u,v)\in E$. The bandwidth of $G$ is the minimum $B(f)$ for all $f$.…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
In 1982 Papadimitriou and Yannakakis introduced the Exact Matching problem, in which given a red and blue edge-colored graph $G$ and an integer $k$ one has to decide whether there exists a perfect matching in $G$ with exactly $k$ red edges.…
We construct a polynomial-time algorithm which given a graph $\Gamma$ finds the full set of non-equivalent Cayley representations of $\Gamma$ over the group $D\cong C_p\times C_{p^k}$, where $p\in\{2,3\}$ and $k\geq 1$. This result implies…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
A set of vertices in a graph forms a potential maximal clique if there exists a minimal chordal completion in which it is a maximal clique. Potential maximal cliques were first introduced as a key tool to obtain an efficient, though…
In this paper, we consider algorithms for edge-coloring multigraphs $G$ of bounded maximum degree, i.e., $\Delta(G) = O(1)$. Shannon's theorem states that any multigraph of maximum degree $\Delta$ can be properly edge-colored with…
Let $G$ be a connected graph on $n$ vertices with adjacency matrix $A_G$. Associated to $G$ is a polynomial $d_G(x_1,\dots, x_n)$ of degree $n$ in $n$ variables, obtained as the determinant of the matrix $M_G(x_1,\dots,x_n)$, where…
We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding…
In recent joint work (2021), we introduced a novel multivariate polynomial attached to every metric space - in particular, to every finite simple connected graph $G$ - and showed it has several attractive properties. First, it is…
The boxicity of a graph $G$ is the minimum dimension $d$ that admits a representation of $G$ as the intersection graph of a family of axis-parallel boxes in $\mathbb{R}^d$. Computing boxicity is an NP-hard problem, and there are few known…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors $V\subseteq\mathbb{R}^d$, we compute a $(1+\varepsilon)$-factor approximation to $\mathop…