Related papers: A Bellman-Ford algorithm for the path-length-weigh…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
We consider a generalized version of the (weighted) one-center problem on graphs. Given an undirected graph $G$ of $n$ vertices and $m$ edges and a positive integer $k\leq n$, the problem aims to find a point in $G$ so that the maximum…
In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
Let $E \subset {\Bbb F}_q^d$, the $d$-dimensional vector space over a finite field with $q$ elements. Construct a graph, called the distance graph of $E$, by letting the vertices be the elements of $E$ and connect a pair of vertices…
We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…
The observed output of an interferometer is the result of interference among the parts of the input light beam traveling along each possible optical path. In complex systems, writing down all these possible optical paths and computing their…
Strong product is an efficient way to construct a larger digraph through some specific small digraphs. The large digraph constructed by the strong product method contains the factor digraphs as its subgraphs, and can retain some good…
We introduce a directed, weighted random graph model, where the edge-weights are independent and beta-distributed with parameters depending on their endpoints. We will show that the row- and column-sums of the transformed edge-weight matrix…
A classical algorithm by Bellman and Ford from the 1950's computes shortest paths in weighted graphs on $n$ vertices and $m$ edges with possibly negative weights in $O(mn)$ time. Indeed, this algorithm is taught regularly in undergraduate…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
The diameter of an undirected unweighted graph $G=(V,E)$ is the maximum value of the distance from any vertex $u$ to another vertex $v$ for $u,v \in V$ where distance i.e. $d(u,v)$ is the length of the shortest path from $u$ to $v$ in $G$.…
Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…
We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called…
We present the first deterministic nearly-linear time algorithm for single-source shortest paths with negative edge weights on directed graphs: given a directed graph $G$ with $n$ vertices, $m$ edges whose weights are integer in…