Cut Star of an Undirected Graph

2021 ◽  
pp. 2150006
Author(s):  
Saeid Hanifehnezhad ◽  
Ardeshir Dolati
Keyword(s):  
Data Structure ◽  
Global Minimum ◽  
Undirected Graph ◽  
Minimum Cut ◽  
New Type

Suppose that [Formula: see text] is an undirected graph. An ordered pair [Formula: see text] of the vertices of the graph [Formula: see text] is called a pendant pair for the graph if [Formula: see text] is a minimum cut separating [Formula: see text] and [Formula: see text] Stoer and Wagner obtained a global minimum cut of [Formula: see text] by using pendant pairs of [Formula: see text] and its contractions. A Gomory Hu tree of the graph [Formula: see text] is a very useful data structure which gives us all the minimum s-t cuts of [Formula: see text] for every pair of distinct vertices [Formula: see text] and [Formula: see text] In this paper, we construct a new type of tree for the graph [Formula: see text] called cut star, by using pendant pairs of [Formula: see text] and its contractions. A cut star of the graph [Formula: see text] is constructed more quickly than a Gomory Hu tree of [Formula: see text] We characterize a class of graphs for which a cut star of a graph of this class is also a Gomory Hu tree.

scholarly journals Parallel Minimum Cuts in Near-linear Work and Low Depth

2021 ◽  
Vol 8 (2) ◽  
pp. 1-20
Author(s):  
Barbara Geissmann ◽  
Lukas Gianinazzi
Keyword(s):  
Data Structure ◽  
Parallel Algorithms ◽  
High Probability ◽  
Spanning Trees ◽  
Undirected Graph ◽  
Randomized Algorithm ◽  
Minimum Cut ◽  
Minimum Cuts ◽  
Maximum Packings

We present the first near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in an undirected graph. Previous parallel algorithms with poly-logarithmic depth required at least quadratic work in the number of vertices. In a graph with n vertices and m edges, our randomized algorithm computes the minimum cut with high probability in O ( m log 4 n ) work and O (log 3 n ) depth. This result is obtained by parallelizing a data structure that aggregates weights along paths in a tree, in addition exploiting the connection between minimum cuts and approximate maximum packings of spanning trees. In addition, our algorithm improves upon bounds on the number of cache misses incurred to compute a minimum cut.

Research on a New Type of Integral Sum Graph with the Sequence Label Method

2013 ◽  
Vol 340 ◽  
pp. 542-545
Author(s):  
Duan Yin Shi ◽  
Xiao Peng Zhang ◽  
Wen Yu Li
Keyword(s):  
Data Structure ◽  
Point Of View ◽  
Graph Labeling ◽  
Practical Point ◽  
Label Method ◽  
Alternative Method ◽  
New Type ◽  
Fan Graph

Integral sum graph was introduced by Harary. This theory is a labeling of graph. From a practical point of view, integral sum graph labeling can be used as a compressed representation of a graph, a data structure for representing the graph, and an alternative method for defining and storing graphs. In this paper, to give an integral sum labeling of fan graph, and to prove that all multiple composite fan graph are integral sum graphs with the sequence label method.

scholarly journals Research on Spatio-temporal Data Construction of Library under the Background of Digital Humanities-Take the Northeast Anti-Japanese United Forces as an example

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Hong Ni ◽  
Baorui Liu
Keyword(s):  
Big Data ◽  
Data Structure ◽  
Cloud Service ◽  
Temporal Data ◽  
Construction Process ◽  
Knowledge Reconstruction ◽  
New Type ◽  
User Demand ◽  
Spatio Temporal ◽  
Cloud Service Platform

This paper from the perspective of multi-dimensional, relational, dynamic this data characteristics and knowledge reconstruction of library spatio-temporal data, Build a cloud service platform for spatio-temporal data of the library?based on the analysis of user demand then discussed its collection, processing, storage and the construction process of user service that provided with the spatio-temporal data. In the era of big data, spatio-temporal data, as a new type of resource, its construction and research enriched and developed traditional data structure relatively.

THREE TECHNIQUES FOR PARALLEL MAINTENANCE OF A MINIMUM SPANNING TREE UNDER BATCH OF UPDATES

1996 ◽  
Vol 06 (02) ◽  
pp. 213-222 ◽  
Author(s):  
PAOLO FERRAGINA ◽  
FABRIZIO LUCCIO
Keyword(s):  
Data Structure ◽  
Parallel Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Undirected Graph ◽  
Batch Size ◽  
Insertions And Deletions ◽  
Erew Pram ◽  
Pram Model ◽  
Proper Values

In this paper we provide three simple techniques to maintain in parallel the minimum spanning tree of an undirected graph under single or batch of edge updates (i.e., insertions and deletions). Our results extend the use of the sparsification data structure to the EREW PRAM model. For proper values of the batch size, our algorithms require less time and work than the best known dynamic parallel algorithms.

Resonator Networks, 1: An Efficient Solution for Factoring High-Dimensional, Distributed Representations of Data Structures

2020 ◽  
Vol 32 (12) ◽  
pp. 2311-2331
Author(s):  
E. Paxon Frady ◽  
Spencer J. Kent ◽  
Bruno A. Olshausen ◽  
Friedrich T. Sommer
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Efficient Solution ◽  
High Dimensional ◽  
Search Problem ◽  
Combinatorial Search ◽  
Distributed Representations ◽  
Factorization Problem ◽  
Analysis And Evaluation ◽  
New Type

The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of cognition. Here we show how this may be accomplished within the framework of Vector Symbolic Architectures (VSAs) (Plate, 1991 ; Gayler, 1998 ; Kanerva, 1996 ), whereby data structures are encoded by combining high-dimensional vectors with operations that together form an algebra on the space of distributed representations. In particular, we propose an efficient solution to a hard combinatorial search problem that arises when decoding elements of a VSA data structure: the factorization of products of multiple codevectors. Our proposed algorithm, called a resonator network, is a new type of recurrent neural network that interleaves VSA multiplication operations and pattern completion. We show in two examples—parsing of a tree-like data structure and parsing of a visual scene—how the factorization problem arises and how the resonator network can solve it. More broadly, resonator networks open the possibility of applying VSAs to myriad artificial intelligence problems in real-world domains. The companion article in this issue (Kent, Frady, Sommer, & Olshausen, 2020 ) presents a rigorous analysis and evaluation of the performance of resonator networks, showing it outperforms alternative approaches.

A New Type of Center Data Structure in Cloud Computing

2014 ◽  
Vol 13 (3) ◽  
pp. 461-468
Author(s):  
Guo Xiaohui ◽  
Wei Jian Yu ◽  
Wang Beibei ◽  
Liyongqing .
Keyword(s):  
Cloud Computing ◽  
Data Structure ◽  
New Type

scholarly journals The Edmonds-Gallai Decomposition for the $k$-Piece Packing Problem

10.37236/1905 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Marek Janata ◽  
Martin Loebl ◽  
Jácint Szabó
Keyword(s):  
Polynomial Algorithm ◽  
Undirected Graph ◽  
Packing Problem ◽  
Matching Problem ◽  
Graph Packing ◽  
Path Packing ◽  
New Type ◽  
Vertex Sets ◽  
Simple Connected Graph ◽  
Type Decomposition

Generalizing Kaneko's long path packing problem, Hartvigsen, Hell and Szabó consider a new type of undirected graph packing problem, called the $k$-piece packing problem. A $k$-piece is a simple, connected graph with highest degree exactly $k$ so in the case $k=1$ we get the classical matching problem. They give a polynomial algorithm, a Tutte-type characterization and a Berge-type minimax formula for the $k$-piece packing problem. However, they leave open the question of an Edmonds-Gallai type decomposition. This paper fills this gap by describing such a decomposition. We also prove that the vertex sets coverable by $k$-piece packings have a certain matroidal structure.

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