Related papers: Sequential Algorithms and Independent Sets Discove…
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational…
The independence number of a sparse random graph G(n,m) of average degree d=2m/n is well-known to be \alpha(G(n,m))~2n ln(d)/d with high probability. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size (1+o(1)) n…
Given a graph $G=(V,E)$, suppose we are interested in selecting a sequence of vertices $(x_j)_{j=1}^n$ such that $\left\{x_1, \dots, x_k\right\}$ is `well-distributed' uniformly in $k$. We describe a greedy algorithm motivated by potential…
The degree distribution is one of the most fundamental properties used in the analysis of massive graphs. There is a large literature on graph sampling, where the goal is to estimate properties (especially the degree distribution) of a…
Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…
The study of the optimality of low-complexity greedy scheduling techniques in wireless communications networks is a very complex problem. The Local Pooling (LoP) factor provides a single-parameter means of expressing the achievable capacity…
Let $G$ be a graph. A set $S \subseteq V(G)$ is independent if its elements are pairwise non-adjacent. A vertex $v \in V(G)$ is shedding if for every independent set $S \subseteq V(G) \setminus N[v]$ there exists $u \in N(v)$ such that $S…
We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary…
We give nearly optimal bounds on the sample complexity of $(\widetilde{\Omega}(\epsilon),\epsilon)$-tolerant testing the $\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random…
We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
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…
We give an $O^*(1.0821^n)$-time, polynomial space algorithm for computing Maximum Independent Set in graphs with bounded degree 3. This improves all the previous running time bounds known for the problem.
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…
We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for…
Finding frequently occurring subgraph patterns or network motifs in neural architectures is crucial for optimizing efficiency, accelerating design, and uncovering structural insights. However, as the subgraph size increases,…
Finding minimum dominating set and maximum independent set for graphs in the classical online setup are notorious due to their disastrous $\Omega(n)$ lower bound of the competitive ratio that even holds for interval graphs, where $n$ is the…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…