Showing papers on "Spanning tree published in 1983"
Book•
01 Jan 1983TL;DR: This paper presents a meta-trees tree model that automates the very labor-intensive and therefore time-heavy and therefore expensive process of manually selecting trees to grow in a graph.
Abstract: Foundations Disjoint Sets Heaps Search Trees Linking and Cutting Trees Minimum Spanning Trees Shortest Paths Network Flows Matchings
2,120 citations
TL;DR: A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights that can be initiated spontaneously at any node or at any subset of nodes.
Abstract: Abstract : A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log of N to the base 2 + 2E and a message contains at most one edge weight plus log of 8N to the base 2 bits. The algorithm can be initiated spontaneously at any node or at any subset of nodes.
1,152 citations
TL;DR: An O(mn log n)-time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse graphs.
1,042 citations
Proceedings Article•
01 Jan 1983
TL;DR: Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph.
184 citations
01 Dec 1983
TL;DR: In this paper, the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph was studied and a data structure for maintaining the data structure and updating the tree was presented.
Abstract: Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph. For the case of a general graph, maintaining the data structure and updating the tree are shown to take O((
139 citations
129 citations
TL;DR: In this paper, a distributed algorithm for constructing minimum weight directed spanning trees (arborescences), each with a distinct root node, in a strongly connected directed graph is presented, and the amount of information exchanged and the time to completion are O(|N|^{2}).
Abstract: A distributed algorithm is presented for constructing minimum weight directed spanning trees (arborescences), each with a distinct root node, in a strongly connected directed graph. A processor exists at each node. Given the weights and origins of the edges incoming to their nodes, the processors follow the algorithm and exchange messages with their neighbors until all arborescences are constructed. The amount of information exchanged and the time to completion are O(|N|^{2}) .
108 citations
TL;DR: In this paper, the minimum number of edges a graph G on n vertices can have so that any tree on N vertices is isomorphic to some spanning tree of G, called such a graph universal for spanning trees.
Abstract: Introduction A number of papers [1,2,3,4,6] recently have been concerned with the following question. What is the minimum number s{n) of edges a graph G on n vertices can have so that any tree on n vertices is isomorphic to some spanning tree of G? We call such a graph universal for spanning trees. Since Kn, the complete graph on n vertices (see [5] for terminology), has the required property, it is immediate that
64 citations
TL;DR: A test of randomness based on the edge length distribution of the Minimal Spanning Tree is presented and it is shown that randomness is higher on the right side of the distribution than the left.
64 citations
TL;DR: This work extends to the multi-constrained, unweighted case, the analysis that was already made in a previous work for the one-conStrained, weighted case of undirected spanning tree problems from the viewpoint of their computational complexity.
48 citations
TL;DR: In this article, a new and simpler method is proposed for counting the spanning trees of a labelled molecular graph, which involves finding the characteristic polynomials of certain graphs (the inner duals) related to, but substantially smaller than, the one whose spanning trees are being enumerated.
Abstract: A new and simpler method is proposed for counting the spanning trees of a labelled molecular-graph. Its application involves finding the characteristic polynomials (or generalized characteristic polynomials) of certain graphs (the inner duals) related to, but substantially smaller than, the one whose spanning trees are being enumerated.
TL;DR: In this article, an algorithmic approach for transforming any spanning tree of a 2-connected graph into any other spanning tree in the graph is presented. But the approach is restricted to the case where the diameter of the spanning tree differs from that of the previous tree by at most one.
Abstract: We give an algorithmic approach for transforming any spanning tree of a 2-connected graph into any other spanning tree of the graph. At each step of the transformation we obtain a spanning tree whose diameter differs from that of the previous tree by at most one. Thus if a 2-connected graph G has a as the minimum and b as the maximum diameter of a spanning tree, then for any integer c between a and b , graph G has a spanning tree of diameter c .
TL;DR: A stochastic version of bottleneck spanning tree problem in which edge costs are random variables is considered, and an algorithm which finds an optimal spanning tree of the original problem in a polynomial order of its problem size is proposed.
Abstract: This paper considers a stochastic version of bottleneck spanning tree problem in which edge costs are random variables. The problem is to find an optimal spanning tree under the chance constraint with respect to bottleneck (maximum cost) edge of spanning tree. The problem is first transformed into a deterministic equivalent problem. Then its subproblem is introduced and a close relation between these problems is clarified. Finally, based on the relation, an algorithm which finds an optimal spanning tree of the original problem in a polynomial order of its problem size is proposed.
TL;DR: The following interpolation theorem is proved: If a graph G contains spanning trees having exactly m and n end-vertices, then for every integer k, m < k < n, G contains a spanning tree having exactly k end- Vertices.
Abstract: The following interpolation theorem is proved: If a graph G contains spanning trees having exactly m and n end-vertices, with m < n, then for every integer k, m < k < n, G contains a spanning tree having exactly k end-vertices. This settles a problem posed by Chartrand at the Fourth International Conference on Graph Theory and Applications held in Kalamazoo, 1980.
01 Aug 1983-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: A simple and efficient curvilinear feature extraction algorithm based on minimum spanning trees of edge points and closely related to Zahn's previous work on Gestalt clustering is described.
Abstract: A simple and efficient curvilinear feature extraction algorithm is described. The algorithm is based on minimum spanning trees of edge points and closely related to Zahn's previous work on Gestalt clustering. Examples drawn from real world images are shown to demonstrate the capabilities and applicabilities of the algorithm. Stimulating interest and inducing application of the algorithm in the areas of computer vision and image understanding are among the major objectives of the paper.
TL;DR: This paper estimates the size of the largest tree almost surely, and proposes two approximate greedy algorithms that achieve a solution whose value is one half of the value of the optimal solution, with high probability.
TL;DR: The empirical performance of the algorithms of Kruskal, Prim, and Sollin for determining a minimum spanning tree is examined and found to be considerably better than suggested by worst case analysis.
TL;DR: The solution of such a problem by a branch-and-bound algorithm base on Lagrangean relaxation is discussed, which aims to construct a minimal cost spanning tree subject to the limitations on the consumption of the scarce resources.
Abstract: : Consider a network in which one node is a source having an infinite supply of a commodity, and every other node is a sink having a known constant demand. Furthermore, associated with each potential arc of the network are the following known constants: the cost of constructing the arc, the amount of each scarce resource consumed during the construction of the arc, and the flow capacity of the arc. Given the above known constants as well as the available supply of each of the scarce resources, the problem is to construct a minimal cost spanning tree subject to the limitations on the consumption of the scarce resources and the requirement that there exists a flow from the source satisfying the demands at the sinks without exceeding any arc capacity. This paper discusses the solution of such a problem by a branch-and-bound algorithm base on Lagrangean relaxation. Also included are applications of the problem, extensions to the problem, and a report on preliminary computational experience with a computer implementation of the algorithm. (Author)
26 Oct 1983
TL;DR: A new image segmentation technique based on minimum spanning trees is proposed, related to Gestalt principles of perceptual organization, which is extremely flexible in accomodating different objectives and criteria of segmentation.
Abstract: A new image segmentation technique based on minimum spanning trees is proposed. The motivation for using minimum spanning trees is their apparent ability of Gestalt clustering, thus relating the segmentation algorithm to Gestalt principles of perceptual organization. Several examples of segmentation using the new algorithm demonstrate the closeness between the results and human perception. The new algorithm is extremely flexible in accomodating different objectives and criteria of segmentation.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: An application of the bucket sort in Kruskal's minimal spanning tree algorithm is proposed, which is very fast if the edge costs are from a distribution which is close to uniform.
TL;DR: Several kinds of optimal spanning trees are characterized and conditions for existence of strongly optimal trees are given and imply previous results of Rosenstiehl and Gale in the case of linear orders or preorders.
TL;DR: The worst case running time of the minimal spanning tree algorithm presented by Bentley and Friedman is shown to be N2 logN, fork≧2 andΘ(N2), fork=1.
Abstract: This paper concerns the worst case running time of the minimal spanning tree algorithm presented by Bentley and Friedman. For a set ofN points ink-dimensional Euclidean space the worst case performance of the algorithm is shown to beΘ(N
2 logN), fork≧2 andΘ(N
2), fork=1.
TL;DR: A set of algorithms to find the spanning trees, the minimal paths and minimal cutsets of a graph, starting from the incidence matrix of the graph is developed, which makes it possible to design small desk top calculators capable of handling reasonably large and complex graphs.
TL;DR: This paper extends and strengthens Quirk and Seymour's result by showing that in a simple binary matroid M the quotient of the number of bases by thenumber of circuits is at least 2.
01 Jan 1983
01 Jan 1983
TL;DR: This dissertation gives O(n) step algorithms for solving a number of graph problems on an n x n array of processors, where n is the number of vertices of the graph under consideration, and shows that a machine where the processors are inter-connected as a binary tree can support all the dictionary and priority priority operations as well as some other data queries.
Abstract: In the last few years, stimulated by the advent of VLSI, many researchers turned their attention to the design of algorithms suited for a parallel processing environment, i.e. to the situation where more than one processor is available. The need for new algorithms arises because an algorithm for solving a particular problem may be time-efficient when implemented on one model of computation and yet be terribly inefficient for another model.
Of particular interest are networks of processors whose geometrical arrangement is simple and regular, since such geometries are ideal for implementation on VLSI chips. This dissertation deals with two such networks: the two-dimensional n x n array of processors, and the complete binary tree of processors.
We give O(n) step algorithms for solving a number of graph problems on an n x n array of processors, where n is the number of vertices of the graph under consideration. The problems considered include: marking the bridges of an undirected graph, marking the articulation points of such a graph, finding the length of a shortest cycle, finding a minimum spanning tree, and a number of other problems.
We also show that a machine where the processors are inter-^connected as a binary tree can support all the dictionary and priority^queue operations as well as some other data queries. Every one of^the operations takes O(logn) steps, where n is the number of keys^present. In addition, a sequence of operations can be pipelined at a^constant rate. In previous designs, either an operation required^(OMEGA)(logN) steps where N is the total capacity of the machine, i.e. the
maximum number of keys that can be stored in it, or O(logn) performance was achieved at the expense of additional wires.
^^*This research was supported by the National Science Foundation under grant MCS-79-05163.
TL;DR: A connected planar graphG legal if it has at least two nodes, no parallel edges or self-loops and at most two terminals (degree 1 nodes) and all terminals and degree 2 nodes are exterior.
Abstract: Call a connected planar graphG legal if it has at least two nodes, no parallel edges or self-loops and at most two terminals (degree 1 nodes) and all terminals and degree 2 nodes are exterior This class of graphs arose in connection with a two-dimensional generating system for modeling growth by binary cell division Showing that any permitted pattern can be generated properly requires a matching or pairing lemma The vertex set of a legal graph withn nodes can be split intop adjacent pairs ands singletons withs p, resulting in a matching which includes at least\(2\left[ {\frac{n}{3}} \right]\) nodes This bound is sharp in the sense that there are legal graphs for which this matching is maximum The matching can be implemented by a linear time algorithm A legal graph witht terminals and n≥4 nodes has a spanning tree with at most\(\left[ {\frac{{n - t}}{2}} \right] + t\) terminals; this bound is sharp Such a spanning tree can be constructed by an algorithm which operates in almost linear time
TL;DR: An algorithm for designing a deadlock-free system with the minimum resource cost is presented, whose running time is bounded by O(ca(m) + mlogm), where the inverse of Ackermann's function, which is very slowly growing.
Abstract: Consider a system consisting of a set ofn processes, P~, P2 . . . . . Pn, and a set of serially reusable resources of m different types, R1, R~ . . . . . R,~. It is assumed that the system is \"claim-limited,\" that is, its \"claim matrix\" C, whose (i, j ) element C(i, j) is the maximum number of units of R: that may be needed by P, at the same time, is known a priori. It is desired to design a deadlock-free system, that is, one which never deadlocks for any allocation sequence within the limits given by C. For j ffi 1, 2 . . . . . m, let a, (>0) be the cost of one unit of Rj. An algorithm for designing a deadlock-free system with the minimum resource cost is presented. Its running time is bounded by O(ca(m) + mlogm), where e ts the number of nonzero elements in C and a, is the inverse of Ackermann's function, which is very slowly growing