Related papers: Space-Efficient Algorithms for Reachability in Geo…
A disk graph is an intersection graph of disks in $\mathbb{R}^2$. Determining the computational complexity of finding a maximum clique in a disk graph is a long-standing open problem. In 1990, Clark, Colbourn, and Johnson gave a…
Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…
A temporal graph is a dynamic graph where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays…
Reachability in hypergraphs is essential for modeling complex groupwise interactions in real-world applications such as co-authorship, social network, and biological analysis, where relationships go beyond pairwise interactions. In this…
A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is modeled by an edge from $A$ to $B$ with starting time "11 a.m." and duration "7…
In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a…
Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
Consider the problem of maintaining source sink reachability($st$-Reachability), single source reachability(SSR) and strongly connected component(SCC) in an edge decremental directed graph. In particular, we design a randomized algorithm…
The efficient and fair distribution of indivisible resources among agents is a common problem in the field of \emph{Multi-Agent-Systems}. We consider a graph-based version of this problem called Reachable Assignments, introduced by Gourves,…
In this paper we focus on the following constrained reachability problem over edge-labeled graphs like RDF -- "given source node x, destination node y, and a sequence of edge labels (a, b, c, d), is there a path between the two nodes such…
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…
A temporal graph $\mathcal{G}=(G,\lambda)$ can be represented by an underlying graph $G=(V,E)$ together with a function $\lambda$ that assigns to each edge $e\in E$ the set of time steps during which $e$ is present. The reachability graph…
In this paper we present an efficient reachability oracle under single-edge or single-vertex failures for planar directed graphs. Specifically, we show that a planar digraph $G$ can be preprocessed in $O(n\log^2{n}/\log\log{n})$ time,…
As one of the fundamental graph operations, reachability queries processing has been extensively studied during the past decades. Many approaches followed the line of designing 2-hop labels to make acceleration. Considering that the index…
A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) \cap Lin(v) \neq \emptyset. Despite their simplicity and elegance, reachability oracles have failed to…
We initiate a systematic study of approximation schemes for fundamental optimization problems on disk graphs, a common generalization of both planar graphs and unit-disk graphs. Our main contribution is a general framework for designing…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
Accessibility, defined as travel impedance between spatially dispersed opportunities for activity, is one of the main determinants of public transport use. In-depth understanding of its properties is crucial for optimal public transport…