Related papers: Effect of Constraint Relaxation on the Minimum Ver…
We consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color. Using the cavity method, we present a detailed and systematic analytical study…
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…
We consider a generalization of the densest subhypergraph problem where nonnegative rewards are given for including partial hyperedges in a dense subhypergraph. Prior work addressed this problem only in cases where reward functions are…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
Problems related to graph matching and isomorphisms are very important both from a theoretical and practical perspective, with applications ranging from image and video analysis to biological and biomedical problems. The graph matching…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that approximates no-slip boundary conditions with rapid linear…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
In this paper we address the graph matching problem. Following the recent works of \cite{zaslavskiy2009path,Vestner2017} we analyze and generalize the idea of concave relaxations. We introduce the concepts of conditionally concave and…
We initiate a systematic study of approximation schemes for fundamental optimization problems on disk graphs, a common generalization of both planar graphs and unit-disk graphs. Our main contribution is a general framework for designing…
We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…
In this paper we study the mincut problem in the online setting. We consider two distinct models: A) competitive analysis and B) regret analysis. In the competitive setting we consider the vertex arrival model; whenever a new vertex arrives…
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…
The feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We…
Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…
This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…
We present an approach to representing large sets of mutual exclusions, also known as mutexes or mutex constraints. These are the types of constraints that specify the exclusion of some properties, events, processes, and so on. They are…
We use convex relaxation techniques to produce lower bounds on the optimal value of subset selection problems and generate good approximate solutions. We then explicitly bound the quality of these relaxations by studying the approximation…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…