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Data-analysis tasks often involve an iterative process, which requires refining previous solutions. For instance, when analyzing dynamic social networks, we may be interested in monitoring the evolution of a community that was identified at…
For a hereditary graph class $\mathcal{H}$, the $\mathcal{H}$-elimination distance of a graph $G$ is the minimum number of rounds needed to reduce $G$ to a member of $\mathcal{H}$ by removing one vertex from each connected component in each…
Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of…
Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…
In a disk graph, every vertex corresponds to a disk in $\mathbb{R}^2$ and two vertices are connected by an edge whenever the two corresponding disks intersect. Disk graphs form an important class of geometric intersection graphs, which…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-$k$-ECSS problem, we are given a graph $G=(V,E)$ whose edges have non-negative…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
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.…
The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph $G$, construct a spanning tree $T$ of $G$ minimizing its maximum edge congestion where the congestion of an edge $e\in T$ is the number of edges $uv$…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
Generalised hypertree width ($ghw$) is a hypergraph parameter that is central to the tractability of many prominent problems with natural hypergraph structure. Computing $ghw$ of a hypergraph is notoriously hard. The decision version of the…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For $m$-edge and $n$-vertex graphs, it is well-known to be solvable in $O(m\sqrt{n})$ time; however, for several applications…
Recently, there has been interest in the question of whether a partial matrix in which many of the fully defined principal submatrices are PSD is approximately PSD completable. These questions are related to graph theory because we can…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical…
Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…
Graph Balancing is the problem of orienting the edges of a weighted multigraph so as to minimize the maximum weighted in-degree. Since the introduction of the problem the best algorithm known achieves an approximation ratio of $1.75$ and it…
In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…