scholarly journals Efficient algorithms for the reverse shortest path problem on trees under the hamming distance

2017 ◽  
Vol 27 (1) ◽  
pp. 46-60 ◽  
Author(s):  
Javad Tayyebi ◽  
Massoud Aman
Keyword(s):  
Shortest Path ◽  
Hamming Distance ◽  
Minimum Cost ◽  
Shortest Path Problem ◽  
Arc Length ◽  
Bound Constraints ◽  
Shortest Distance ◽  
Special Cases ◽  
Minimum Cost Flow Problem ◽  
Minimum Cut Problem

Given a network G(V,A,c) and a collection of origin-destination pairs with prescribed values, the reverse shortest path problem is to modify the arc length vector c as little as possible under some bound constraints such that the shortest distance between each origin-destination pair is upper bounded by the corresponding prescribed value. It is known that the reverse shortest path problem is NP-hard even on trees when the arc length modifications are measured by the weighted sum-type Hamming distance. In this paper, we consider two special cases of this problem which are polynomially solvable. The first is the case with uniform lengths. It is shown that this case transforms to a minimum cost flow problem on an auxiliary network. An efficient algorithm is also proposed for solving this case under the unit sum-type Hamming distance. The second case considered is the problem without bound constraints. It is shown that this case is reduced to a minimum cut problem on a tree-like network. Therefore, both cases studied can be solved in strongly polynomial time.

Linearizable Special Cases of the Quadratic Shortest Path Problem

2021 ◽  
pp. 245-256
Author(s):  
Eranda Çela ◽  
Bettina Klinz ◽  
Stefan Lendl ◽  
James B. Orlin ◽  
Gerhard J. Woeginger ◽  
...  
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Special Cases

scholarly journals A genetic algorithm for the fuzzy shortest path problem in a fuzzy network

2020 ◽  
Author(s):  
Lihua Lin ◽  
Chuzheng Wu ◽  
Li Ma
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Ad Hoc ◽  
Real Life ◽  
Shortest Path Problem ◽  
Arc Length ◽  
Routing Problem ◽  
Path Lengths ◽  
Fuzzy Network ◽  
Arc Lengths

Abstract The shortest path problem (SPP) is an optimization problem of determining a path between specified source vertex s and destination vertex t in a fuzzy network. Fuzzy logic can handle the uncertainties, associated with the information of any real life problem, where conventional mathematical models may fail to reveal proper result. In classical SPP, real numbers are used to represent the arc length of the network. However, the uncertainties related with the linguistic description of arc length in SPP are not properly represented by real number. We need to address two main matters in SPP with fuzzy arc lengths. The first matter is how to calculate the path length using fuzzy addition operation and the second matter is how to compare the two different path lengths denoted by fuzzy parameter. We use the graded mean integration technique of triangular fuzzy numbers to solve this two problems. A common heuristic algorithm to solve the SPP is the genetic algorithm. In this manuscript, we have introduced an algorithmic method based on genetic algorithm for determining the shortest path between a source vertex s and destination vertex t in a fuzzy graph with fuzzy arc lengths in SPP. A new crossover and mutation is introduced to solve this SPP. We also describe the QoS routing problem in a wireless ad hoc network.

scholarly journals MENENTUKAN RUTE TERPENDEK DENGAN MENGGUNAKAN ALGORITMA FLOYD-WARSHALL DALAM PENDISTRIBUSIAN BARANG PADA PT. RAPY RAY PUTRATAMA

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
M Ridwan Mukti ◽  
Mulyono . .
Keyword(s):  
Shortest Path ◽  
Minimum Distance ◽  
Shortest Path Problem ◽  
Search Result ◽  
Shortest Route ◽  
Shortest Distance ◽  
Path Search ◽  
Distance Data ◽  
Shortest Path Search ◽  
Route Search

ABSTRAKMasalah pendistribusian pada perusahaan adalah masalah yang sangat penting untuk diperhatikan. Pada dasarnya pendistribusian barang akan sangat menghemat perusahaan dalam berbagai hal.Pencarian rute terpendek yang dilakukan pada PT. Rapy Ray Putratama Medan dilakukan dengan menghubungkan berbagai macem outlet dan juga termasuk beberapa outletnya adalah PT. Rapy Ray Putratama cabang medan. Permasalah rute terpendek ini dapat disesaikan dengan menggunakan salah satu metode pencarian rute terpendek yaitu algoritma Floyd-Warshall. Penelitian ini bertujuan untuk mengetahui hasil dari rute yang akan dipilih sebagai saran atau masukan kepada Perusahaan. Untuk hasil pencarian rute terpendek dengan menggunakan algoritma Floyd-Warshallyang diimplementasikan dalam pemrograman Codeblocks:: adalah jarak dari PT ke outlet maupun dari outlet ke outlet memiliki jarak yang paling minimum. Setelah itu, dapat ditentukan rute terpendek yang akan dipilih oleh salesman dalam pendistribusian yang telah didapatkan pada program tersebut. Data yang diinput adalah data jarak. Output yang dihasilkan program adalah jarak terpendek. Dengan penghematan jarak yang telah dilakukan. Pembentukan rute usulan yang dihasilkan dengan menggunakan metode algoritma Floyd-Warshall menghasilkan rute yang lebih dekat dengan total jarak penghematan adalah 10.97 % (51.304 km).Kata kunci: Pendistribusian, Pencarian rute terpendek, algoritma Floyd-Warshall. ABSTRACTThe problem of distribution to the company is a very important issue to notice. Basically the distribution of goods will greatly save the company expense in various ways. The searching for the shortest route done at PT. Rapy Ray Putratama Medan conducted by connecting various kinds of outlets and also including some outlets at PT. Rapy Ray Putratama Medan branch. This shortest path problem can be solved by using one of the shortest path search methods the Floyd-Warshall algorithm. This study aims to determine the results of the route to be selected as advice or input to the company. For the shortest route search result using Floyd-Warshall algorithm implemented in codeblocks programming is the distance from PT. Rapy Ray Putratamata outlet and from outlet to outlet which has the minimum distance. Subsequently, it can be determined the shortest route that will be selected by the salesman in the distribution that has been attained on the program. The inputted data is the distance data. The output produced by the program is the shortest distance by saving the distance that has been done through the algorithm. The proposed route formatted using the Floyd-Warshall algorithm method resulted in a route closer to the total distance of a saving distance of 10.97% (51,304 km). Keywords: Distribution, the shortest path searching, Floyd-Warshall algorithm.

scholarly journals The Capacity Expansion Path Problem in Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jianping Li ◽  
Juanping Zhu
Keyword(s):  
Shortest Path ◽  
Polynomial Algorithm ◽  
Shortest Paths ◽  
Minimum Cost ◽  
Capacity Expansion ◽  
Shortest Path Problem ◽  
Strongly Polynomial Algorithm ◽  
Minimum Number ◽  
Expansion Path ◽  
Strongly Polynomial

This paper considers the general capacity expansion path problem (GCEP) for the telecommunication operators. We investigate the polynomial equivalence between the GCEP problem and the constrained shortest path problem (CSP) and present a pseudopolynomial algorithm for the GCEP problem, no matter the graph is acyclic or not. Furthermore, we investigate two special versions of the GCEP problem. For the minimum number arc capacity expansion path problem (MN-CEP), we give a strongly polynomial algorithm based on the dynamic programming. For the minimum-cost capacity expansion shortest path problem (MCESP), we give a strongly polynomial algorithm by constructing a shortest paths network.

scholarly journals Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1360
Author(s):  
Lehua Yang ◽  
Dongmei Li ◽  
Ruipu Tan
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Neutrosophic Set ◽  
Uncertain Environments ◽  
Shortest Distance ◽  
Edge Distance ◽  
Neutrosophic Graph ◽  
Axis Of Symmetry ◽  
Constituent Elements ◽  
Scientific Fields

The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.

The Shortest Path Problem Research Based on the Green Traffic

2015 ◽  
Vol 744-746 ◽  
pp. 2126-2130 ◽  
Author(s):  
Bao You Liu ◽  
Nan Xi Jin
Keyword(s):  
Shortest Path ◽  
Operational Research ◽  
Optimization Problems ◽  
Real Life ◽  
Shortest Path Problem ◽  
Practical Significance ◽  
Research Model ◽  
Low Carbon ◽  
Shortest Distance ◽  
Super League

"Advocate the low carbon travel and create the green traffic" is a hot topic in today's society. In order to explore the optimal travel route in 13 China football association super league cities, an operational research model based on the shortest path problem was put forward and resolved by Lingo 11.0 software. The study indicates that the shortest distance traveling each China football association super league city in order in ideal transportation conditions is 9596.000 km. While, considering the traffic restriction of Beijing-Shijiazhuang highway and Beijing-Tianjin highway, the optimized shortest distance is 9693.000 km. This study has a certain practical significance in solving transportation optimization problems in real life.

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