Filters








31,259 Hits in 4.5 sec

Minimum Spanning trees with Neighborhoods [article]

Víctor Blanco, Elena Fernández, Justo Puerto
2016 arXiv   pre-print
This paper studies Minimum Spanning Trees under incomplete information for its vertices.  ...  are measured with a ℓ_q-norm.  ...  Feasible solutions to the Minimum Spanning Tree with Neighborhoods (MSTN) problem consist of a set of points, Y * = {y v ∈ N v | v ∈ V }, together with a spanning tree T * on the graph G * = (Y * , E *  ... 
arXiv:1611.02918v1 fatcat:humlhpau2faapp3ljxohy4rlhu

On Minimum- and Maximum-Weight Minimum Spanning Trees with Neighborhoods

Reza Dorrigiv, Robert Fraser, Meng He, Shahin Kamali, Akitoshi Kawamura, Alejandro López-Ortiz, Diego Seco
2014 Theory of Computing Systems  
The minimum weight version of the problem is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem, and the maximum weight version (max-MSTN) has not been studied previously A preliminary  ...  We study optimization problems for the Euclidean Minimum Spanning Tree (MST) problem on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input.  ...  The minimum weight MST version of the problem has been studied previously, and is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem.  ... 
doi:10.1007/s00224-014-9591-3 fatcat:54x7lbihkvdmval35r3mpuxvdm

On Minimum-and Maximum-Weight Minimum Spanning Trees with Neighborhoods [chapter]

Reza Dorrigiv, Robert Fraser, Meng He, Shahin Kamali, Akitoshi Kawamura, Alejandro López-Ortiz, Diego Seco
2013 Lecture Notes in Computer Science  
The minimum weight version of the problem is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem, and the maximum weight version (max-MSTN) has not been studied previously A preliminary  ...  We study optimization problems for the Euclidean Minimum Spanning Tree (MST) problem on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input.  ...  The minimum weight MST version of the problem has been studied previously, and is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem.  ... 
doi:10.1007/978-3-642-38016-7_9 fatcat:3ijd5lqgdffs3fziett4froat4

Rectilinear Shortest Path and Rectilinear Minimum Spanning Tree with Neighborhoods [chapter]

Yann Disser, Matúš Mihalák, Sandro Montanari, Peter Widmayer
2014 Lecture Notes in Computer Science  
The Minimum Spanning Tree Problem with Neighborhoods asks to find a placement p such that the cost of a resulting minimum spanning tree is minimum among all graphs Gp.  ...  We study these problems in the L1 metric, and show that the shortest path problem with neighborhoods is solvable in polynomial time, whereas the minimum spanning tree problem with neighborhoods is APX-hard  ...  Minimum Spanning Tree with Neighborhoods In the Minimum Spanning Tree Problem with Neighborhoods, or MSTN, we are given a set of regions R = {R 1 , . . . , R n } and an underlying graph G = (R, E).  ... 
doi:10.1007/978-3-319-09174-7_18 fatcat:xbeeiwgslrepdjxns7krfhaquq

The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees

Kenneth J. Supowit
1983 Journal of the ACM  
We show that a necessary and sufficient condition for G*(S) to exhibit the edge-inclusion property is that G*(S) be the minimal spanning tree (MST) of S.  ...  Given a convex polygon with its vertices arbitrarily colored with two colors, find the closest pair of vertices of opposite colors. Close refers again to smallest euclidean distance.  ...  Optimal Algorithms for Computing the Minimum Distance Between Two Finite Planar Sets Godfried T. Toussaint and Binay K.  ... 
doi:10.1145/2402.322386 fatcat:knncv4rvw5ea7f4hre5lr2x5gq

Minimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods

Víctor Blanco, Elena Fernández, Justo Puerto
2017 European Journal of Operational Research  
This paper studies Minimum Spanning Trees under incomplete information assuming that it is only known that vertices belong to some neighborhoods that are second order cone representable and distances are  ...  measured with a q -norm.  ...  Feasible solutions to the Minimum Spanning Tree with Neighborhoods (MSTN) problem consist of a set of points, Y * = {y v ∈ N v | v ∈ V }, together with a spanning tree T * on the graph G * = (Y * , E *  ... 
doi:10.1016/j.ejor.2017.04.023 fatcat:3sactbnphze6ljq6mngzfuspcq

Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem

Bin Hu, Markus Leitner, Günther R. Raidl
2007 Journal of Heuristics  
We consider the generalized version of the classical Minimum Spanning Tree problem where the nodes of a graph are partitioned into clusters and exactly one node from each cluster must be connected.  ...  Tests on Euclidean and random instances with up to 1280 nodes indicate especially on instances with many nodes per cluster significant advantages over previously published metaheuristic approaches.  ...  Introduction The Generalized Minimum Spanning Tree (GMST) problem is an extension of the classical Minimum Spanning Tree (MST) problem and is defined as follows.  ... 
doi:10.1007/s10732-007-9047-x fatcat:dg5l4fh4pzh6zhwjpggk5cz3hi

IMMERSIVE VISUALIZATION OF THE QUALITY OF DIMENSIONALITY REDUCTION

M. Babaee, M. Datcu, G. Rigoll
2013 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
We visualize the Minimum Spanning Tree (MST) of neighborhood graphs of data before and after dimensionality reduction in an immersive 3D virtual environment.  ...  The results show that a specific dimension reduction technique exhibits different performance in dealing with different datasets.  ...  IMMERSIVE VISUALIZATION Minimum Spanning Tree The Minimum Spanning Tree is a spanning tree of an edge-weighted graph whose weight is minimum among the weight of other span-ning trees (Sedgewick, 2002  ... 
doi:10.5194/isprsarchives-xl-1-w3-67-2013 fatcat:cndrt6xoizgrlfipnlxfyljpcu

On the Euclidean Minimum Spanning Tree Problem

Sanguthevar Rajasekaran
2005 Computing Letters  
Finding a minimum spanning tree for this graph is known as the Euclidean minimum spanning tree problem (EMSTP).  ...  The minimum spanning tree algorithms alluded to before will run in time O(n 2 ) (or nearly O(n 2 )) on this graph.  ...  If these edges together with E are enough to produce a minimum spanning tree for all the input points, we output this and quit.  ... 
doi:10.1163/1574040053326325 fatcat:6mizupy3pbg5bfkpeyq6d564pq

Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem

Ravindra K. Ahuja, James B. Orlin, Dushyant Sharma
2001 Mathematical programming  
The capacitated miinimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node.  ...  The size of each of these neighborhood structures grows exponentially with the problem size without any substantial increase in the computational times needed to find improved neighbors.  ...  For any node i, we denote by Existing neighborhood structures Neighbo A neighborhood search algorithm for the capacitated minimum spanning tree problem starts with a feasible tree T.  ... 
doi:10.1007/s101070100234 fatcat:mgr6upawpndarhi6jr5abl6t3q

Secure Key Exchange and Encryption Mechanism for Group Communication in Wireless Ad Hoc Networks

Sumathy S, Upendra Kumar B
2010 International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks  
The nodes are organized in spanning tree fashion, as they avoid forming cycles and exchange of key occurs only with authenticated neighbors in ad hoc networks, where nodes join or leave the network dynamically  ...  the minimum spanning tree is constructed as inFigure 3.  ...  This mechanism requires the nodes to be organized in a spanning tree fashion as spanning tree is constructed with minimum distance which can cover all the nodes without forming a cycle.  ... 
doi:10.5121/jgraphhoc.2010.2102 fatcat:36xuwegfkzbdtnrm3itill2avq

Minimal vertex separators and new characterizations for dually chordal graphs

Pablo De Caria, Marisa Gutierrez
2009 Electronic Notes in Discrete Mathematics  
Minimal vertex separators and new characterizations for dually chordal graphs T is a spanning tree and each minimal vertex separator of G induces a subtree of G .  ...  Minimal vertex separators and new characterizations for dually chordal graphs T is a spanning tree and each minimal vertex separator of G induces a subtree of G .  ...  If a tree is compatible with G then each minimal vertex separator induces a subtree. If each minimal vertex separator induces a subtree in a spanning tree T for G then T is compatible with G .  ... 
doi:10.1016/j.endm.2009.11.022 fatcat:nskoy7ayxbb6dkfedkl2r5lcx4

The conditional neighborhood for graph and its algorithm

2013 IOSR Journal of Mathematics  
We will prove that the neighborhood will be give different neighborhood by different algorithm.  ...  In this paper we will define the conditional neighborhood for graph and classified the conditions into many types. In each type we will compute the algorithm for graph .  ...  spanning tree by using Kruskal's algorithm we have: And minimum spanning tree will be: The conditional neighborhood for graph and its algorithm.  ... 
doi:10.9790/5728-0843341 fatcat:c2qhgzarhzev3b7zylrfqwetfi

A Fast Approximation Algorithm For Minimum Spanning Trees In K-Dimensional Space

P.M. Vaidya
1984 25th Annual Symposium onFoundations of Computer Science, 1984.  
A fast algorithm, which finds an approximate minimum spanning tree with wei h t a t most (1+c) times optimal in developed for the L" q =2,3, ..., distance metrics.  ...  We study the problem of finding a minimum spanning tree on the complete graph on n points in E', with the weight of an edge between any two points being the distance between the two points under some distance  ...  Introduction Given an undirected graph with a weight assigned to each edge, a minimum spanning tree (MST) is a spanning tree whose edges have a minimum total weight among all spanning trees.  ... 
doi:10.1109/sfcs.1984.715941 dblp:conf/focs/Vaidya84 fatcat:4ia5uscdf5d5vcvqlt245d4fly

Page 1588 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Summary: “The capacitated minimum spanning tree problem is to find a minimum cost spanning tree in a network where nodes have specified demands, with an additional capacity constraint on the subtrees incident  ...  structure for the capacitated minimum spanning tree problem.  ... 
« Previous Showing results 1 — 15 out of 31,259 results