Related papers: Polynomial Time Algorithms for Tracking Path Probl…
For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of $G$ that is not a shortest $uv$-path of $G$. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known…
It is $\mathsf{NP}$-hard to determine the minimum number of branching vertices needed in a single-source distance-preserving subgraph of an undirected graph. We show that this problem can be solved in polynomial time if the input graph is…
Given a graph with edge costs and vertex profits and given a budget B, the Orienteering Problem asks for a walk of cost at most B of maximum profit. Additionally, each profit may be given with a time window within it can be collected by the…
We show that finding minimally intersecting $n$ paths from $s$ to $t$ in a directed graph or $n$ perfect matchings in a bipartite graph can be done in polynomial time. This holds more generally for unimodular set systems.
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where the goal is to construct a graph that satisfies certain…
We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. We show that it is NP-complete to decide whether a graph has an orientation such that…
We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on $n$ vertices. Our algorithm solves a more general problem: given $n$ and $\omega$ as input, it computes the number of…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
Strongly chordal graphs are a subclass of chordal graphs. The interest in this subclass stems from the fact that many problems which are NP-complete for chordal graphs are solvable in polynomial time for this subclass. However, we are not…
Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence,…
In this paper, we consider different constrained partition problems for weighted trees and cactus graphs. We focus on the (l,u)-partition problem, which is the problem of partitioning a weighted graph into connected clusters such that each…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
We initiate a general study of what we call orientation completion problems. For a fixed class C of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in…
A polynomial time algorithm which detects all paths and cycles of all lengths in form of vertex pairs (start, finish).
We study the problem of planning paths for a team of robots for visually monitoring an environment. Our work is motivated by surveillance and persistent monitoring applications. We are given a set of target points in a polygonal environment…
We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a {\em…
Removing all connections between two vertices s and z in a graph by removing a minimum number of vertices is a fundamental problem in algorithmic graph theory. This (s,z)-separation problem is well-known to be polynomial solvable and serves…
Given an undirected graph $G=(V,E)$, vertices $s,t\in V$, and an integer $k$, Tracking Shortest Paths requires deciding whether there exists a set of $k$ vertices $T\subseteq V$ such that for any two distinct shortest paths between $s$ and…
We propose a consistent polynomial-time method for the unseeded node matching problem for networks with smooth underlying structures. Despite widely conjectured by the research community that the structured graph matching problem to be…
Given an edge-weighted undirected graph and a list of k source-sink pairs of vertices, the well-known minimum multicut problem consists in selecting a minimum-weight set of edges whose removal leaves no path between every source and its…