Related papers: Metro-Line Crossing Minimization: Hardness, Approx…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is…
The maximum matching width is a graph width parameter that is defined on a branch-decomposition over the vertex set of a graph. In this short paper, we prove that the problem of computing the maximum matching width is NP-hard.
In Terminal Monitoring Set (TMS), the input is an undirected graph $G=(V,E)$, together with a collection $T$ of terminal pairs and the goal is to find a subset $S$ of minimum size that hits a shortest path between every pair of terminals.…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
We study the directed maximum common edge subgraph problem (DMCES) for the class of directed graphs that are finite, weakly connected, oriented, and simple. We use DMCES to define a metric on partially ordered sets that can be represented…
In the {\em capacitated} survivable network design problem (Cap-SNDP), we are given an undirected multi-graph where each edge has a capacity and a cost. The goal is to find a minimum cost subset of edges that satisfies a given set of…
We study the Minimum Sum Vertex Cover problem, which asks for an ordering of vertices in a graph that minimizes the total cover time of edges. In particular, n vertices of the graph are visited according to an ordering, and for each edge…
The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
Metro or transit maps, are schematic representations of transit networks to facilitate effective route-finding. These maps are often advertised on a web page or pamphlet highlighting routes from source to destination stations. To visually…
We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs: * testing if an undirected graph has a perfect matching (this implies lower…
We study the Minimum Shared Edges problem introduced by Omran et al. [Journal of Combinatorial Optimization, 2015] on planar graphs: Planar MSE asks, given a planar graph G = (V,E), two distinct vertices s,t in V , and two integers p, k,…
This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional…
We study the classical Node-Disjoint Paths (NDP) problem: given an $n$-vertex graph $G$ and a collection $M=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of vertices of $G$ called demand pairs, find a maximum-cardinality set of node-disjoint…
In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph $G=(V,E)$, consisting of a vertex set $V$ of size $n$ and an edge set $E$. Each vertex in $V$ is assigned a color from the set…
Given a collection $L$ of line segments, we consider its arrangement and study the problem of covering all cells with line segments of $L$. That is, we want to find a minimum-size set $L'$ of line segments such that every cell in the…
In modern applications of graphs algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied. Hence, it is desirable to use…