Related papers: Resource-Constrained Shortest Path with Polytopic …
We propose an algorithm for solving the time-dependent shortest path problem in flow fields where the FIFO (first-in-first-out) assumption is violated. This problem variant is important for autonomous vehicles in the ocean, for example,…
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
We formulate and study the thinnest path problem in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of…
We present several results in the CONGEST model on round complexity for Replacement Paths (RPaths), Minimum Weight Cycle (MWC), and All Nodes Shortest Cycles (ANSC). We study these fundamental problems in both directed and undirected…
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…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such…
We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
The concept of Reload cost in a graph refers to the cost that occurs while traversing a vertex via two of its incident edges. This cost is uniquely determined by the colors of the two edges. This concept has various applications in…
The Resource Constrained Shortest Path Problem (RCSPP) is a fundamental combinatorial optimisation problem in which the goal is to find a least-cost path in a directed graph subject to one or more resource constraints. In this paper we…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
We investigate the problem of computing the top-$k$ simple shortest paths in weighted digraphs. While the single-pair variant -- finding the top-$k$ simple shortest paths between two specified vertices -- has been extensively studied over…
We introduce and study a novel problem of computing a shortest path tree with a minimum number of non-terminals. It can be viewed as an (unweighted) Steiner Shortest Path Tree (SSPT) that spans a given set of terminal vertices by shortest…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…
The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can…