Related papers: Exact solutions to the Weighted Region Problem
Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t in R^2, where the…
The weighted region problem is the problem of finding the weighted shortest path on a plane consisting of polygonal regions with different weights. For the case when the plane is tessellated by squares, we can solve the problem…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
We consider the problem of computing an approximate weighted shortest path in a weighted subdivision, with weights assigned from the set $\{0, 1, \infty\}$. We present a data structure $B$, which stores a set of convex, non-overlapping…
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 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…
This paper presents an approximation algorithm for finding a shortest path between two points $s$ and $t$ in a weighted planar subdivision $\PS$. Each face $f$ of $\PS$ is associated with a weight $w_f$, and the cost of travel along a line…
Link weights are the principal parameters of shortest path routing protocols, the most commonly used protocols for IP networks. The problem of optimally setting link weights for unique shortest path routing is addressed. Due to the…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
A {\em parametric weighted graph} is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edge-weighted graph. Parametric weighted graph…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
We want to investigate 'spaces' where paths have a 'weight', or 'cost', expressing length, duration, price, energy, etc. The weight function is not assumed to be invariant up to path-reversion. Thus, 'weighted algebraic topology' can be…
Finding shortest paths in a given network (e.g., a computer network or a road network) is a well-studied task with many applications. We consider this task under the presence of an adversary, who can manipulate the network by perturbing its…
This paper investigates the problem of computing the shortest path between two states under resource constraints in environments with resource-replenishment regions. Namely, the length of the path is limited by a budget that can be restored…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
In this paper we address two different related problems. We first study the problem of finding a simple shortest path in a $d$-dimensional real space subdivided in several polyhedra endowed with different $\ell_p$-norms. This problem is a…
We discuss two versions of the Fr\'echet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance…
The on-line shortest path problem is considered under various models of partial monitoring. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way, a decision maker has to choose in each…
In this paper, we present efficient algorithms for the single-source shortest path problem in weighted disk graphs. A disk graph is the intersection graph of a family of disks in the plane. Here, the weight of an edge is defined as the…
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…