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About 8,457 papers for “Shortest path problem”

Incremental Shortest-Path Problem

G. Ramalingam, Thomas Reps, G. Ramalingam · 2008

The grammar problem, a generalization of the single-source shortest-path problem introduced by Knuth, is to compute the minimum-cost derivation of a terminal string from each non-terminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the single-source shortest-path problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortest-path problem is its ability to handle “multiple heterogeneous modifications”: between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edge-length changes.

Cited by 0

The Shortest Path Problem

Camil Demetrescu, Andrew V. Goldberg, David S. Johnson · DIMACS series in discrete mathematics and theoretical computer science · 2009

Shortest path problems are among the most fundamental combinatorial optimization problems with many applications, both direct and as subroutines. They arise naturally in a remarkable number of real-world settings. A limited list includes transportation planning, network optimization, packet routing, image segmentation, speech recognition, document formatting, robotics, compilers, traffic information systems, and dataflow analysis. Shortest path algorithms have been studied since the 1950's and still remain an active area of research. This volume reports on the research carried out by participants during the Ninth DIMACS Implementation Challenge, which led to several improvements of the state of the art in shortest path algorithms. The infrastructure developed during the Challenge facilitated further research in the area, leading to substantial follow-up work as well as to better and more uniform experimental standards. The results of the Challenge included new cutting-edge techniques for emerging applications such as GPS navigation systems, providing experimental evidence of the most effective algorithms in several real-world settings.

Cited by 132

The Shortest-Path Problem

Hector Ortega‐Arranz, Diego R. Llanos, Arturo González-Escribano · Synthesis lectures on theoretical computer science · 2015

Cited by 13

The Shortest Path Problem

Piet Van Mieghem · Cambridge University Press eBooks · 2006

The shortest path problem asks for the computation of the path from a source to a destination node that minimizes the sum of the positive weights of its constituent links. The related shortest path tree (SPT) is the union of the shortest paths from a source node to a set of m other nodes in the graph with N nodes. If m = N − 1, the SPT connects all nodes and is termed a spanning tree. The SPT belongs to the fundamentals of graph theory and has many applications. Moreover, powerful shortest path algorithms like that of Dijkstra exist. Section 15.7 studied the hopcount, the number of hops (links) in the shortest path, in sparse graphs with unit link weights. In this chapter, the influence of the link weight structure on the properties of the SPT will be analyzed. Starting from one of the simplest possible graph models, the complete graph with i.i.d. exponential link weight, the characteristics of the shortest path will be derived and compared to Internet measurements.

Cited by 1

All Colors Shortest Path Problem

Yunus Can Bilge, Dogukan Çagatay, Begüm Genç et al. · arXiv (Cornell University) · 2015

All Colors Shortest Path problem defined on an undirected graph aims at finding a shortest, possibly non-simple, path where every color occurs at least once, assuming that each vertex in the graph is associated with a color known in advance. To the best of our knowledge, this paper is the first to define and investigate this problem. Even though the problem is computationally similar to generalized minimum spanning tree, and the generalized traveling salesman problems, allowing for non-simple paths where a node may be visited multiple times makes All Colors Shortest Path problem novel and computationally unique. In this paper we prove that All Colors Shortest Path problem is NP-hard, and does not lend itself to a constant factor approximation. We also propose several heuristic solutions for this problem based on LP-relaxation, simulated annealing, ant colony optimization, and genetic algorithm, and provide extensive simulations for a comparative analysis of them. The heuristics presented are not the standard implementations of the well known heuristic algorithms, but rather sophisticated models tailored for the problem in hand. This fact is acknowledged by the very promising results reported.

Cited by 7Open access

The quadratic shortest path problem

Salman Ali · Summit (Simon Fraser University) · 2019

Quadratic Shortest Path Problem (QSPP) is a variation of the Shortest Path problem, where the objective function is quadratic. In addition to a cost associated with each edge in a graph, there is a cost with each pair of edges in the graph. The cost of a path is the sum of the costs of each edge in the path and the quadratic costs for each pair of edges in the path. This makes the problem NP-hard. polynomial-time algorithms are known for restricted versions of QSPP, such as Adjacent-QSPP, where the quadratic cost is only considered between adjacent pairs of vertices in the path. Integer programs with different bounds have also been discussed for QSPP with non-negative cost matrices. In this thesis, we provide integer programs for solving QSPP with arbitrary cost matrices. We compare our formulation where sub-tours are eliminated with the well-known MTZ constraints with one where sub-tours are eliminated iteratively by introducing the violated constraints only. We also provide two heuristic polynomial time solutions to the QSPP, the Basic Algorithm and the Multi Start Algorithm. We compare the Multi Start Algorithm with solutions obtained from the integer programs with MTZ constraints and show that the Multi Start Algorithm is a good heuristic to QSPP.

Cited by 0Open access

Weighted Region Shortest Path Problem

John Reif, Zheng Sun · 2007

In this paper we present an approximation algorithm for solving the following optimal motion planning problem: Given a planar space composed of polygonal regions, each of which is associated with a positive unit weight, and two points s and t, find a path from s to t with the minimum weight, where the weight of a path is defined to be the weighted sum of the lengths of the sub-paths within each region. Some of the previous works on this problem involve constructing a discretization of the planar space and then computing the approximate paths in the discretized space. Discretizations used by these works include uniform and non-uniform discretizations. Our algorithm adopts discretizations proposed by previous work and presents improvement in computing optimal paths in the discretized space by using a "discretized wavefront" method. Compared to the previous work, our algorithm has the following three advantages: (a) can compute exact solutions for a discrete case of this problem; (b) can...

Cited by 0

$K$ Constrained Shortest Path Problem

Ning Shi · IEEE Transactions on Automation Science and Engineering · 2009

Motivated by a real project for a sophisticated automated storage and retrieval system (AS/RS), we study the problem of generating K shortest paths that are required to satisfy a set of constraints. We propose a structural branching procedure that decomposes the problem into at most K|N| subproblems, where |N| is the number of nodes in the network. By using a Network Modification procedure, each subproblem can be transformed into a constrained shortest path problem (CSP). When these constraints satisfy a so called separable property, the subproblem can be further simplified. Based on this branching procedure, we propose a specific algorithm for an application where resource and loopless constraints have to be respected. Numerical results show that our algorithm is very efficient and robust.

Cited by 22

Bounded Acceleration Shortest Path Problem

Stefano Ardizzoni, Luca Consolini, Mattia Laurini et al. · OSF Preprints (OSF Preprints) · 2022

MATLAB simulation for paper "Shortest path with acceleration constraints: Complexity and approximation algorithms" on Computational Optimization and Applications

Cited by 0

The Generalized Shortest Path Problem

Vladimir Batagelj, Franz J. Brandenburg, Patrice Ossona De Mendez et al. · 2007

this paper we show that the generalized shortest path problem can be solved efficiently for multiplicative weights. The solution is running Dijkstra's algorithm in reverse. In the case of additive weights there is a dynamic programming approach and a pseudo-polynomial algorithm. Finally, if there are restrictions both on the cost and on the weight of a path, then a simple reduction of PARTITION shows that the constrained shortest path problem is NP-complete. This fact was already known from [1].

Cited by 0

Motivation Problem Formulation Shortest Path Problem (SPP)

Dmitry Yershov, Steve Lavalle · 2011

X f ree xI • Work or configuration space Rn • Polyhedral obstacles Xobs ⊂ Rn Xfree = Rn \\Xobs (N vertices) • Goal set Xgoal ⊂ Xfree • Initial configuration xI ∈ Xfree • Find the shortest path x ̃ : [0, 1] → Xfree • 2D problem can be solved in N log(N) time [Hershberger and Suri, 1999] • 3D problem is NP-hard

Cited by 0

Clustered Shortest-Path Tree Problem Instances

Thanh Pham Dinh · Mendeley Data · 2022

+ The tested data for Clustered Shortest-Path Tree Problem. + The tested data were created based on the MOM of the Clustered Traveling Salesman Problem (https://www.sciencedirect.com/science/article/pii/S0305054812002122) + Get from: D:\OneDrive - moet.edu.vn\MyData\Read\Source code\10. MFO\W. Benchmarks\04.Clustered_Tree_Instance_From_Clustered_TSP\Instances\Clustered_Tree_instances\MOM_Lib

Cited by 0Open access