Related papers: Finding an induced path that is not a shortest pat…
Let $S$ be a set of $n$ points in a polygon $P$ with $m$ vertices. The geodesic unit-disk graph $G(S)$ induced by $S$ has vertex set $S$ and contains an edge between two vertices whenever their geodesic distance in $P$ is at most one. In…
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…
The problem of finding the shortest path in a graph G(V, E) has been widely studied. However, in many applications it is necessary to compute an arbitrary number of them, k. Even though the problem has raised a lot of interest from…
We develop the methodology of positioning graph vertices relative to each other to solve the problem of determining isomorphism of two undirected graphs. Based on the position of the vertex in one of the graphs, it is determined the…
An odd hole in a graph is a induced cycle with odd length greater than 3. In an earlier paper (with Sophie Spirkl), solving a longstanding open problem, we gave a polynomial-time algorithm to test if a graph has an odd hole. We subsequently…
A directed graph $G$ is called a pumpkin if $G$ is a union of induced paths with a common start vertex $s$ and a common end vertex $t$, and the internal vertices of every two paths are disjoint. We give an algorithm that given a directed…
We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$. This…
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…
The replacement paths problem for directed graphs is to find for given nodes s and t and every edge e on the shortest path between them, the shortest path between s and t which avoids e. For unweighted directed graphs on n vertices, the…
Given in the plane a set $S$ of $n$ points and a set of disks centered at these points, the disk graph $G(S)$ induced by these disks has vertex set $S$ and an edge between two vertices if their disks intersect. Note that the disks may have…
We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
We investigate the problem of computing the shortest secure path in a Voronoi diagram. Here, a path is secure if it is a sequence of touching Voronoi cells, where each Voronoi cell in the path has a uniform cost of being secured.…
For each integer $\ell \geq 4$, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least $\ell$ and even
Let us say a graph is $s\mathcal{O}$-free, where $s\ge 1$ is an integer, if there do not exist $s$ cycles of the graph that are pairwise vertex-disjoint and have no edges joining them. The structure of such graphs, even when $s=2$, is not…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
We describe a polynomial time algorithm for, given an undirected graph G, finding the minimum dimension d such that G may be isometrically embedded into the d-dimensional integer lattice Z^d.
For each integer $t\ge 5$, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least $t$ and odd.
We give polynomial-time algorithms for obtaining hamilton circuits in random graphs, G, and random directed graphs, D. If n is finite, we assume that G or D contains a hamilton circuit. If G is an arbitrary graph containing a hamilton…
Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes…