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Minimum cut bases in undirected networks

Florentine Bunke, Horst W. Hamacher, Francesco Maffioli, Anne M. Schwahn
2010 Discrete Applied Mathematics  
Given an 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.  ... 
doi:10.1016/j.dam.2009.07.015 fatcat:xx7m2fz7vfaw7ms6cxkht7fbau

Novel Approximation Algorithm for Calculating Maximum Flow in a Graph

Madhu Lakshmi, Pradeep Kumar Kaushik, Nitin Arora
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.  ... 
doi:10.5120/12864-9693 fatcat:xc3vuka6wfaw3bki7xguc7g6m4

On Mimicking Networks Representing Minimum Terminal Cuts [article]

Arindam Khan, Prasad Raghavendra, Prasad Tetali, László A. Végh
2012 arXiv   pre-print
equal to the size of the 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  ... 
arXiv:1207.6371v1 fatcat:jmkj7tocuvhs5jbbl6qs4g25aa

Novel Bounded Binary-Addition Tree Algorithm for Binary-State Network Reliability Problems [article]

Wei-Chang Yeh
2020 arXiv   pre-print
Many 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.  ... 
arXiv:2011.14832v1 fatcat:e7lfjacxkfgv5kyc5274julxvi

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

Masatoshi Sato, Hisashi Aomori, Mamoru Tanaka
2014 Journal of Signal Processing  
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  ... 
doi:10.2299/jsp.18.259 fatcat:fjgk7q732nhzfgqzyr7jlzxwpu

New mathematical model for finding minimum vertex cut set

Tina Beseri Sevim, Hakan Kutucu, Murat Ersen Berberler
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.  ... 
doi:10.1109/icpci.2012.6486469 fatcat:vzofvsutcjfxdps4t7d6adq53a

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 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  ... 
doi:10.1587/transfun.e97.a.2317 fatcat:gujc7vvx25d6beh5kyekpyac2u

Efficient Algorithms for the Problems of Enumerating Cuts by Non-decreasing Weights

Li-Pu Yeh, Biing-Feng Wang, Hsin-Hao Su
2009 Algorithmica  
For example, for the 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 .  ... 
doi:10.1007/s00453-009-9284-5 fatcat:ufqesc363vawxpwfz45melhx2y

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

Zongpeng Li, Baochun Li, Lap Chi Lau
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.  ... 
doi:10.1109/tit.2008.2011516 fatcat:pf6qktx5i5fthdjlvngfy4hi7q

A New Technique for Finding Min-cut Tree

Ashwani Kumar, Surinder Pal Singh, Nitin Arora
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.  ... 
doi:10.5120/12084-9170 fatcat:5q4t3kwukzgqdkelu47t7klzwi

The Cost Advantage of Network Coding in Uniform Combinatorial Networks

Andrew Smith, Bryce Evans, Zongpeng Li, Baochun Li
2008 2008 5th IEEE Annual Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks Workshops  
We investigate this fundamental question 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.  ... 
doi:10.1109/sahcnw.2008.24 fatcat:eu7b5ltta5fslez2dlag6v3rjm

A Distributed Algorithm for Min-Max Tree and Max-Min Cut Problems in Communication Networks

Song Guo, Victor C M Leung
2010 IEEE/ACM Transactions on Networking  
., the maximum-lifetime multicast problem 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.  ... 
doi:10.1109/tnet.2009.2038998 fatcat:4fbsmwwezneyvg4aiffd5lspce

Incremental minimum spanning tree algorithms

Laura Ciupala, Adrian Deaconu, Delia Spridon
Sometimes the weighted graph 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.  ... 
doi:10.31926/but.mif.2020. fatcat:ci2srf4xfbbz3ksanhhwu73hpu

Theoretical and computational advances for network diversion

Christopher A. Cullenbine, R. Kevin Wood, Alexandra M. Newman
2013 Networks  
This problem, with intelligence-gathering and war-fighting applications, seeks a 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.  ... 
doi:10.1002/net.21514 fatcat:gmabxdmfj5hbje56uiuk5ox2de
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