Related papers: Composable Core-sets for Determinant Maximization …
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…
Given a simple, undirected graph $G$ with a threshold function $\tau:V(G) \rightarrow \mathbb{N}$, the \textsc{Target Set Selection} (TSS) problem is about choosing a minimum cardinality set, say $S \subseteq V(G)$, such that starting a…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for…
We study the problem of finding unitary submatrices of the $N \times N$ discrete Fourier transform matrix, in the context of interpolating a discrete bandlimited signal using an orthogonal basis. This problem is related to a diverse set of…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
In this paper, we study two popular variants of Graph Coloring -- Dominator Coloring and CD Coloring. In both problems, we are given a graph $G$ and a natural number $\ell$ as input and the goal is to properly color the vertices with at…
This work studies the parameterized complexity of finding secluded solutions to classical combinatorial optimization problems on graphs such as finding minimum s-t separators, feedback vertex sets, dominating sets, maximum independent sets,…
Spectral methods which represent data points by eigenvectors of kernel matrices or graph Laplacian matrices have been a primary tool in unsupervised data analysis. In many application scenarios, parametrizing the spectral embedding by a…
Let $\mathcal{G}_{n, \beta^*}$ $(\mathcal{G}^*_{n,\beta^*})$ be the set of all (connected) graphs of order $n$ with fractional matching number $\beta^*$. In this paper, the graphs with maximal spectral radius in $\mathcal{G}_{n,\beta^*}$…
For any undirected graph $G=(V,E)$ and a set $E_W$ of candidate edges with $E\cap E_W=\emptyset$, the $(k,\gamma)$-spectral augmentability problem is to find a set $F$ of $k$ edges from $E_W$ with appropriate weighting, such that the…
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is…
Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose…
Let $G = (V,E)$ be an undirected graph with maximum degree $\Delta$ and vertex conductance $\Psi^*(G)$. We show that there exists a symmetric, stochastic matrix $P$, with off-diagonal entries supported on $E$, whose spectral gap…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
The diameter of a graph is one if its most important parameters, being used in many real-word applications. In particular, the diameter dictates how fast information can spread throughout data and communication networks. Thus, it is a…
Given a hypergraph $H$, the Planar Support problem asks whether there is a planar graph $G$ on the same vertex set as $H$ such that each hyperedge induces a connected subgraph of $G$. Planar Support is motivated by applications in graph…
We study the parameterized complexity of the connected version of the vertex cover problem, where the solution set has to induce a connected subgraph. Although this problem does not admit a polynomial kernel for general graphs (unless NP is…
One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound…