scholarly journals Approximation Complexity of min-max (Regret) Versions of Shortest Path, Spanning Tree, and Knapsack

2005 ◽  
pp. 862-873 ◽  
Author(s):  
Hassene Aissi ◽  
Cristina Bazgan ◽  
Daniel Vanderpooten
Keyword(s):  
Shortest Path ◽  
Spanning Tree ◽  
Approximation Complexity

scholarly journals A Constant-Factor Approximation for the Generalized Cable-Trench Problem

2019 ◽  
Author(s):  
Marcelo Benedito ◽  
Lehilton Pedrosa ◽  
Hugo Rosado
Keyword(s):  
Shortest Path ◽  
Steiner Tree ◽  
Spanning Tree ◽  
Optimization Problem ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
Constant Factor ◽  
Steiner Tree Problem ◽  
Negative Factor ◽  
Path Lengths

In the Cable-Trench Problem (CTP), the objective is to find a rooted spanning tree of a weighted graph that minimizes the length of the tree, scaled by a non-negative factor , plus the sum of all shortest-path lengths from the root, scaled by another non-negative factor. This is an intermediate optimization problem between the Single-Destination Shortest Path Problem and the Minimum Spanning Tree Problem. In this extended abstract, we consider the Generalized CTP (GCTP), in which some vertices need not be connected to the root, but may serve as cost-saving merging points; this variant also generalizes the Steiner Tree Problem. We present an 8.599-approximation algorithm for GCTP. Before this paper, no constant approximation for the standard CTP was known.

scholarly journals Some Theoretical Links Between Shortest Path Filters and Minimum Spanning Tree Filters

2019 ◽  
Vol 61 (6) ◽  
pp. 745-762
Author(s):  
Sravan Danda ◽  
Aditya Challa ◽  
B. S. Daya Sagar ◽  
Laurent Najman
Keyword(s):  
Shortest Path ◽  
Spanning Tree ◽  
Minimum Spanning Tree

scholarly journals Choquet-based optimisation in multiobjective shortest path and spanning tree problems

2010 ◽  
Vol 204 (2) ◽  
pp. 303-315 ◽  
Author(s):  
Lucie Galand ◽  
Patrice Perny ◽  
Olivier Spanjaard
Keyword(s):  
Shortest Path ◽  
Spanning Tree

scholarly journals The Implementation of Kruskal’s Algorithm for Minimum Spanning Tree in a Graph

2021 ◽  
Vol 348 ◽  
pp. 01001
Author(s):  
Paryati ◽  
Krit Salahddine
Keyword(s):  
Shortest Path ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Dijkstra’S Algorithm ◽  
Dijkstra Algorithm ◽  
Application System ◽  
Path Creation ◽  
Dijkstra's Algorithm

Kruskal’s Algorithm is an algorithm used to find the minimum spanning tree in graphical connectivity that provides the option to continue processing the least-weighted margins. In the Kruskal algorithm, ordering the weight of the ribs makes it easy to find the shortest path. This algorithm is independent in nature which will facilitate and improve path creation. Based on the results of the application system trials that have been carried out in testing and comparisons between the Kruskal algorithm and the Dijkstra algorithm, the following conclusions can be drawn: that a strength that is the existence of weight sorting will facilitate the search for the shortest path. And considering the characteristics of Kruskal’s independent algorithm, it will facilitate and improve the formation of the path. The weakness of the Kruskal algorithm is that if the number of nodes is very large, it will be slower than Dijkstra’s algorithm because it has to sort thousands of vertices first, then form a path.

Vertex collisions in 3-periodic nets of genus 4

2018 ◽  
Vol 74 (5) ◽  
pp. 600-607 ◽  
Author(s):  
Montauban Moreira de Oliveira Jr ◽  
Geovane Matheus Lemes Andrade ◽  
Eliel Roger da Silva ◽  
Jean-Guillaume Eon
Keyword(s):  
Crystal Structures ◽  
Shortest Path ◽  
Spanning Tree ◽  
Complete List ◽  
Systematic Analysis ◽  
Quotient Graph ◽  
Centre Of Gravity ◽  
Approximate Models ◽  
Barycentric Representation ◽  
Zero Voltage

Unstable nets, by definition, display vertex collisions in any barycentric representation, among which are approximate models for the associated crystal structures. This means that different vertex lattices happen to superimpose when every vertex of a periodic net is located at the centre of gravity of its first neighbours. Non-crystallographic nets are known to be unstable, but crystallographic nets can also be unstable and general conditions for instability are not known. Moreover, examples of unstable nets are still scarce. This article presents a systematic analysis of unstable 3-periodic nets of genus 4, satisfying the restrictions that, in a suitable basis, (i) their labelled quotient graph contains a spanning tree with zero voltage and (ii) voltage coordinates belong to the set {−1, 0, 1}. These nets have been defined by a unique circuit of null voltage in the quotient graph. They have been characterized through a shortest path between colliding vertices. The quotient graph and the nature of the net obtained after identification of colliding vertices, if known, are also provided. The complete list of the respective unstable nets, with a detailed description of the results, can be found in the supporting information.

An oriented spanning tree based genetic algorithm for multi-criteria shortest path problems

2012 ◽  
Vol 12 (1) ◽  
pp. 506-515 ◽  
Author(s):  
Linzhong Liu ◽  
Haibo Mu ◽  
Xinfeng Yang ◽  
Ruichun He ◽  
Yinzhen Li
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Spanning Tree ◽  
Shortest Path Problems

scholarly journals CONSTRUCTING DEGREE-3 SPANNERS WITH OTHER SPARSENESS PROPERTIES

1996 ◽  
Vol 07 (02) ◽  
pp. 121-135 ◽  
Author(s):  
GAUTAM DAS ◽  
PAUL J. HEFFERNAN
Keyword(s):  
Euclidean Space ◽  
Shortest Path ◽  
Spanning Tree ◽  
Maximum Degree ◽  
Euclidean Distance ◽  
Minimum Spanning Tree ◽  
Dimensional Euclidean Space ◽  
Edge Weight

Let V be any set of n points in k-dimensional Euclidean space. A subgraph of the complete Euclidean graph is a t-spanner if for all u and υ in V, the length of the shortest path from u to υ in the spanner is at most t times the Euclidean distance between u and υ. We show that for any δ>1, there exists a t-spanner (where t is a constant that depends only on δ and k) with the following properties: its maximum degree is 3, it has at most n·δ edges, its total edge weight is at most O(1) times the weight of the minimum spanning tree of V, and it can be constructed in O(n log n) time. The constants implicit in the O-notation depend on δ and k.

scholarly journals Prim and Floyd-Warshall Comparative Algorithms in Shortest Path Problem

2018 ◽  
Author(s):  
Andysah Putera Utama Siahaan ◽  
Mesran Mesran
Keyword(s):  
Shortest Path ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Minimum Spanning Tree Problem ◽  
Number Of Branches

Optimization is an effort to obtain the best results by considering the constraints, constraints, and limitations that exist on a problem; the goal is to minimize or suppress the things that harm and maximize the things that are considered profitable. Generally, the Floyd-Warsall algorithm is widely used to solve shortest path problems, while the Prim algorithm is often used to solve the MST (Minimum Spanning Tree) problem in the Graph to minimize tree ranges or reduce the number of branches. Comparing the Prim algorithm with the Floyd-Warsall algorithm is expected to add proof if the Prim algorithm is not only used to solve Minimum Spanning Tree problem but can also solve the problem of Shortest Path Problem.

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