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In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Since a spatial distribution of communication requests is inhomogeneous and related to a population, in constructing a network, it is crucial for delivering packets on short paths through the links between proximity nodes and for…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
In the NP-hard Optimizing PD with Dependencies (PDD) problem, the input consists of a phylogenetic tree $T$ over a set of taxa $X$, a food-web that describes the prey-predator relationships in $X$, and integers $k$ and $D$. The task is to…
In the Maximum-size Properly Colored Forest problem, we are given an edge-colored undirected graph and the goal is to find a properly colored forest with as many edges as possible. We study this problem within a broader framework by…
Notable recent works have focused on the multi-layer properties of coevolving diseases. We point out that very similar systems play an important role in population ecology. Specifically we study a meta food-web model that was recently…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
In this paper we address the problem of computing a sparse subgraph of a weighted directed graph such that the exact distances from a designated source vertex to all other vertices are preserved under bounded weight increment. Finding a…
A geographic network is a graph whose vertices are restricted to lie in a prescribed region in the plane. In this paper we begin to study the following fundamental problem for geographic networks: can a given geographic network be drawn…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
We consider the minimization of edge-crossings in geometric drawings of graphs $G=(V, E)$, i.e., in drawings where each edge is depicted as a line segment. The respective decision problem is NP-hard [Bienstock, '91]. In contrast to theory…
Shortest paths problems are subject to extensive studies in classic distributed models such as the CONGEST or Congested Clique. These models dictate how nodes may communicate in order to determine shortest paths in a distributed input…
Semi-random processes involve an adaptive decision-maker, whose goal is to achieve some predetermined objective in an online randomized environment. They have algorithmic implications in various areas of computer science, as well as…
Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the…
Spatial ecological networks are widely used to model interactions between georeferenced biological entities (e.g., populations or communities). The analysis of such data often leads to a two-step approach where groups containing similar…