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Minimum cut bases in undirected networks

2010
*
Discrete Applied Mathematics
*

Given an

doi:10.1016/j.dam.2009.07.015
fatcat:xx7m2fz7vfaw7ms6cxkht7fbau
*undirected*, connected*network*G = (V, E) with weights on the edges, the*cut*basis problem is asking for a maximal number of linear independent*cuts*such that the sum of the*cut*weights is minimized ... For the unconstrained case, where the*cuts**in*the basis can be of an arbitrary kind, the problem can be written as a multiterminal*network*flow problem and is thus solvable*in*strongly polynomial time. ... Another interesting area is the generalization of the presented formulations for fundamental*cut**bases*to fundamental circuit*bases**in*binary matroids. ...##
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Novel Approximation Algorithm for Calculating Maximum Flow in a Graph

2013
*
International Journal of Computer Applications
*

*In*this paper a new approximation algorithm for calculating the min-

*cut*tree of an

*undirected*edgeweighted graph has been proposed. ... This algorithm is implemented

*in*JAVA language and checked for many input cases. ... APPLICATIONS Reliability of Communication

*Networks*: The problem of finding the

*minimum*

*cut*

*in*a graph plays an important role

*in*the design of communication

*networks*. ...

##
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On Mimicking Networks Representing Minimum Terminal Cuts
[article]

2012
*
arXiv
*
pre-print

equal to the size of the

arXiv:1207.6371v1
fatcat:jmkj7tocuvhs5jbbl6qs4g25aa
*minimum**cut*separating U from K-U*in*H. ... Given a capacitated*undirected*graph G=(V,E) with a set of terminals K ⊂ V, a mimicking*network*is a smaller graph H=(V_H,E_H) that exactly preserves all the*minimum**cuts*between the terminals. ... Contraction-*Based*Mimicking*Networks*Here we will show that on every graph G that has unique*minimum*terminal*cuts*, Algorithm 1 produces a mimicking*network*that is optimal among all contraction-*based*...##
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Novel Bounded Binary-Addition Tree Algorithm for Binary-State Network Reliability Problems
[article]

2020
*
arXiv
*
pre-print

Many

arXiv:2011.14832v1
fatcat:e7lfjacxkfgv5kyc5274julxvi
*network*applications are*based*on binary-state*networks*, where each component has one of two states: success or failure. ... Moreover, we show that replacing each*undirected*arc with two directed arcs, which is required*in*traditional direct methods, is unnecessary*in*the proposed algorithm. ...*minimum**cuts**in*XFC(1:k) for all k. ...##
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A Study of Minimum s-t Cut Algorithm Using Maximum-Flow Neural Network on Directed / Undirected Graphs

Maximum-Flow Neural Network を用いた有向/ 無向グラフに対する最小s-t カットアルゴリズムの一検討

2014
*
Journal of Signal Processing
*

Maximum-Flow Neural Network を用いた有向/ 無向グラフに対する最小s-t カットアルゴリズムの一検討

*In*this paper, we propose a novel

*minimum*

*cut*solution using MF-NN

*in*directed and

*undirected*graphs. ... Keywords: maximum-flow neural

*network*, nonlinear resistive circuit analysis,

*minimum*

*cut*maximum adjacency ordering method [6] 1956 ... 1 Fig.11 Flow

*network*2 Fig. 12 12 Wiring of MF-NN

*in*

*undirected*graph Table 1 1 Each node voltage obtained from analysis node number S-point 1 2 3 4 node voltage (V) 10.00 9.25 8.85 9.33 ...

##
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New mathematical model for finding minimum vertex cut set

2012
*
2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI)
*

*In*this paper, we consider the vertex separator problem. Given an

*undirected*graph G, the vertex separator problem consists

*in*identifying a

*minimum*number of vertex set whose removal disconnects G. ... Afterwards, Karger [6] presented an algorithm for finding the

*minimum*

*cut*of an

*undirected*graph

*in*O(n2log3n) time. The algorithm does more than find a single

*minimum*

*cut*; it finds all of them. ... Hao and Orlin [5] proposed an algorithm to compute the maximum flow problem running

*in*O(mnlog n2/m) time

*in*either a directed or an

*undirected*

*network*. ...

##
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Probabilistic Analysis on Minimum s-t Cut Capacity of Random Graphs with Specified Degree Distribution

2014
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

The capacity (or maximum flow) of an unicast

doi:10.1587/transfun.e97.a.2317
fatcat:gujc7vvx25d6beh5kyekpyac2u
*network*is known to be equal to the*minimum*s-t*cut*capacity due to the max-flow min-*cut*theorem. ...*In*this paper, we present a probabilistic analysis for evaluating the accumulate distribution of the*minimum*s-t*cut*capacity on random graphs. ...*In*order to obtain an insight for statistical properties of the*minimum*s-t*cut*capacity for such random*networks*, it is natural to investigate statistical properties of*minimum*s-t*cut*capacity over a ...##
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Efficient Algorithms for the Problems of Enumerating Cuts by Non-decreasing Weights

2009
*
Algorithmica
*

For example, for the

doi:10.1007/s00453-009-9284-5
fatcat:ufqesc363vawxpwfz45melhx2y
*minimum*k-*cut*problem, the upper bound is immediately reduced by a factor ofÕ(n) for k = 3, 4, 5, 6. ...*In*this paper, we study the problems of enumerating*cuts*of a graph by non-decreasing weights. ... A*minimum**cut*of G is a*cut*of*minimum*weight. As an illustrative example, consider the*undirected*graph*in*Fig. 1 . ...##
###
Page 7572 of Mathematical Reviews Vol. , Issue 98M
[page]

1998
*
Mathematical Reviews
*

Summary: “This paper presents algorithms for computing a min- imum 3-way

*cut*and a*minimum*4-way*cut*of an*undirected*weighted graph G. ...*In*this paper, we first show some prop- erties On*minimum*3-way*cuts*and*minimum*4-way*cuts*, which indicate a recursive structure of the*minimum*k-way*cut*prob- lem when k = 3 and 4. ...##
###
A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks

2009
*
IEEE Transactions on Information Theory
*

*In*this paper, we prove that

*in*

*undirected*

*networks*, the ratio of achievable multicast throughput with

*network*coding to that without

*network*coding is bounded by a constant ratio of 2, i.e.,

*network*coding ... This constant bound 2 represents the tightest bound that has been proved so far

*in*general

*undirected*settings, and is to be contrasted with the unbounded potential of

*network*coding

*in*improving multicast ... Connectivity λ(N ) becomes the size of the

*minimum*simple

*cut*of the

*network*. ...

##
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A New Technique for Finding Min-cut Tree

2013
*
International Journal of Computer Applications
*

*In*this paper we propose a new approximation algorithm for calculating the min-

*cut*tree of an

*undirected*edge-weighted graph. ... Moreover

*in*the unsuccessful cases, the deviation from actual result is very less (usually for less than 5% pairs) and for most of the pairs we obtain correct values of max-flow or min-

*cut*. ... Gomory and Hu [3] solved the multi-terminal

*network*flow problem

*in*1961 and proved that maxflow problems

*in*an

*undirected*

*network*have at most n-1 distinct solutions. ...

##
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The Cost Advantage of Network Coding in Uniform Combinatorial Networks

2008
*
2008 5th IEEE Annual Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks Workshops
*

We investigate this fundamental question

doi:10.1109/sahcnw.2008.24
fatcat:eu7b5ltta5fslez2dlag6v3rjm
*in*the classic*undirected**network*model. ... After almost a decade of research*in**network*coding, so far all known*networks*where such potential exists are*based*on a special class of topologies known as combinatorial*networks*. ... = n k Therefore, by the MIN-*CUT*MAX-FLOW theorem, the*minimum*possible cost for unit flow*in*C n,k is n k + n k Lemma III.3. ...##
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A Distributed Algorithm for Min-Max Tree and Max-Min Cut Problems in Communication Networks

2010
*
IEEE/ACM Transactions on Networking
*

., the maximum-lifetime multicast problem

doi:10.1109/tnet.2009.2038998
fatcat:4fbsmwwezneyvg4aiffd5lspce
*in*multihop wireless*networks*,*in*the data*networking*community. ...*In*random*networks*with n nodes and m arcs, our theoretical analysis shows that the expected communication complexity of our distributed algorithm is*in*the order of O(m). ... This conclusion is*based*on the well-known findings*in*[5] that the*minimum*spanning tree is a min-max spanning tree, but not vice versa,*in**undirected*graphs. ...##
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Incremental minimum spanning tree algorithms

2020
*
SERIES III - MATEMATICS, INFORMATICS, PHYSICS
*

Sometimes the weighted graph

doi:10.31926/but.mif.2020.13.62.1.25
fatcat:ci2srf4xfbbz3ksanhhwu73hpu
*in*which we need to determine a*minimum*spanning tree differs from another weighted graph,*in*which a*minimum*spanning tree is already established, only by an edge weight ( ... We will describe algorithms that determine*minimum*spanning trees*in*the new weighted graphs starting from a*minimum*spanning tree*in*the original weighted graph. 2000 Mathematics Subject Classification ... N, A )*in*the original*network*G*in*O(m) time. ...##
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Theoretical and computational advances for network diversion

2013
*
Networks
*

This problem, with intelligence-gathering and war-fighting applications, seeks a

doi:10.1002/net.21514
fatcat:gmabxdmfj5hbje56uiuk5ox2de
*minimum*-weight, minimal s-t*cut*E C ⊆ E*in*G such that e ∈ E C . ... The*network*-diversion problem (ND) is defined on a directed or*undirected*graph G = (V , E ) having nonnegative edge weights, a source vertex s, a sink vertex t , and a "diversion edge" e . ... Subsequently, Erken [15] develops a combinatorial algorithm, which is*based*on enumerating near-*minimum*-weight s-t*cuts*. ...
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