Related papers: Randomized greedy algorithm for independent sets i…
We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive…
In this paper a greedy algorithm to detect conflict cliques in interval graphs and circular-arc graphs is analyzed. In a graph, a stable set requires that at most one vertex is chosen for each edge. It is equivalent to requiring that at…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
We study the k-wise independent relaxation of the usual model G(N,p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any…
Data-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this experimental evidence, no detailed theory has yet been…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
We study the algorithmic decidability of the domination number in the Erdos-Renyi random graph model $G(n,p)$. We show that for a carefully chosen edge probability $p=p(n)$, the domination problem exhibits a strong irreducible property.…
Motivated by online advertisement and exchange settings, greedy randomized algorithms for the maximum matching problem have been studied, in which the algorithm makes (random) decisions that are essentially oblivious to the input graph. Any…
Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin-Tetali, and Zhao) that the independence polynomial of a $d$-regular graph is maximized by disjoint copies of…
In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
We study the Independent Set (IS) problem in $H$-free graphs, i.e., graphs excluding some fixed graph $H$ as an induced subgraph. We prove several inapproximability results both for polynomial-time and parameterized algorithms.…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
We study robust versions of properties of $(n,d,\lambda)$-graphs, namely, the property of a random sparsification of an $(n,d,\lambda)$-graph, where each edge is retained with probability $p$ independently. We prove such results for the…
The rate of convergence of the classical Thresholding Greedy Algorithm with respect to bases is studied in this paper. We bound the error of approximation by the product of both norms -- the norm of $f$ and the $A_1$-norm of $f$. We obtain…
An $n$-vertex, $d$-regular graph can have at most $2^{n/2+o_d(n)}$ independent sets. In this paper we address what happens with this upper bound when we impose the further condition that the graph has independence number at most $\alpha$.…
Recently, variants of many classical extremal theorems have been proved in the random environment. We, complementing existing results, extend the Erd\H{o}s-Gallai Theorem in random graphs. In particular, we determine, up to a constant…
Given a locally finite graph $\Gamma$, an amenable subgroup $G$ of graph automorphisms acting freely and almost transitively on its vertices, and a $G$-invariant activity function $\lambda$, consider the free energy $f_G(\Gamma,\lambda)$ of…
Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on weighted graphs, termed GreedyMatching.…
For each $N\geq 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\{1,2, ..., N\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N$ goes to infinity of correlation functions: $$ \mathfrak…