Related papers: A Faster Branching Algorithm for the Maximum $k$-D…
Given an undirected graph $G$, the Densest $k$-subgraph problem (DkS) asks to compute a set $S \subset V$ of cardinality $\left\lvert S\right\rvert \leq k$ such that the weight of edges inside $S$ is maximized. This is a fundamental NP-hard…
The maximum genus $\gamma_M(G)$ of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal…
Markov Networks are widely used through out computer vision and machine learning. An important subclass are the Associative Markov Networks which are used in a wide variety of applications. For these networks a good approximate minimum cost…
Given a graph on $n$ vertices and an integer $k$, the feedback vertex set problem asks for the deletion of at most $k$ vertices to make the graph acyclic. We show that a greedy branching algorithm, which always branches on an undecided…
The performance of distributed averaging depends heavily on the underlying topology. In various fields, including compressed sensing, multi-party computation, and abstract graph theory, graphs may be expected to be free of short cycles,…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…
In the last decade, algorithmic frameworks based on a structural graph parameter called mim-width have been developed to solve generally NP-hard problems. However, it is known that the frameworks cannot be applied to the Clique problem, and…
The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…
Given an undirected graph $G$, a quasi-clique is a subgraph of $G$ whose density is at least $\gamma$ $(0 < \gamma \leq 1)$. Two optimization problems can be defined for quasi-cliques: the Maximum Quasi-Clique (MQC) Problem, which finds a…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…
We propose a multi-stage learning approach for pruning the search space of maximum clique enumeration, a fundamental computationally difficult problem arising in various network analysis tasks. In each stage, our approach learns the…
We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…
We consider a connected undirected graph $G(n,m)$ with $n$ nodes and $m$ edges. A $k$-dominating set $D$ in $G$ is a set of nodes having the property that every node in $G$ is at most $k$ edges away from at least one node in $D$. Finding a…
A disk graph is an intersection graph of disks in the Euclidean plane, where the disks correspond to the vertices of the graph and a pair of vertices are adjacent if and only if their corresponding disks intersect. The problem of…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…