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Minimum T-cuts and optimal T-pairings

2002
*
Discrete Mathematics
*

We introduce the notion of

doi:10.1016/s0012-365x(02)00397-7
fatcat:wgyvoah4hjbpnfddeodkwsbwoq
*T*-*pairing**and*give a min-max characterization for the*minimum*size of a*T*-*cut*. ... We show that the coe cients in the minimal TDI system for the*T*-*cut*polyhedron can be arbitrarily big. ... Their suggestions*and*advice signiÿcantly helped improving the presentation. I also thank ZoltÃ an Szigeti*and*AndrÃ as Sebő who were among the ÿrst to encourage me on these results. ...##
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On the Robustness of Distributed Computing Networks
[article]

2021
*
arXiv
*
pre-print

We define

arXiv:1901.02636v3
fatcat:k5lpbcshw5drfhjrmg3obyulpi
*cut*metrics that measure the connectivity,*and*show a non-zero gap between the maximum flow*and*the*minimum**cut*. ... We develop mathematical programs to compute the*optimal*interdiction,*and*polynomial-time approximation algorithms that achieve near-*optimal*interdiction in simulation. ... In a traditional flow network, the maximum flow between a source-destination (s −*t*)*pair*equals the*minimum**cut*, which is the*minimum*-capacity link removals that disconnect the s −*t**pair*[17] . ...##
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An optimal graph theoretic approach to data clustering: theory and its application to image segmentation

1993
*
IEEE Transactions on Pattern Analysis and Machine Intelligence
*

For graphs of moderate size (-2000 vertices), the

doi:10.1109/34.244673
fatcat:eisqkbw7vbfmhc6wje326zlsga
*optimal*solution is obtained through partitioning a flow*and**cut*equivalent tree of 6, which can be efficiently constructed using the Gomory-Hu algorithm ... The segmentation is achieved by effectively searching for closed contours of edge elements (equivalent to*minimum**cuts*in G), which consist mostly of strong edges, while rejecting contours containing isolated ... Let (V, --*t*vm) be a*minimum**cut*with the smallest*cut*value among all*minimum**cuts*separating each*pair*of vertices of 6,*and*let*T**and**T*' be any other*pair*of vertices. ...##
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Parametric min-cuts analysis in a network

2003
*
Discrete Applied Mathematics
*

The all

doi:10.1016/s0166-218x(02)00496-1
fatcat:bgx4lxltdrfsfn2cg66vw2umem
*pairs**minimum**cuts*problem in a capacitated undirected network is well known. ... Gomory*and*Hu showed that the all*pairs**minimum**cuts*are revealed by a min-*cut*tree that can be obtained by solving exactly (n − 1) maximum ow problems, where n is the number of nodes in the network. ... Recall that*T*1 is a min-*cut*tree in G( ),*and*hence provides*cuts*with*minimum*cardinality between every*pair*of nodes. ...##
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Reduced power expenditure in the minimum latency transmission scheduling problem

2014
*
2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP)
*

The

doi:10.1109/isccsp.2014.6877851
dblp:conf/isccsp/DeliparaschosCC14
fatcat:idrzlvwi75h3hgj6kmc3iip4eq
*Cutting*Plane algorithm used is evaluated with regard to its performance*and*the outcome is that the power expenditure is reduced significantly, while achieving the*minimum*latency transmission scheduling ... In this paper, a*Cutting*Plane approach is proposed in order to combine the*minimum*latency transmission scheduling problem with power expenditure minimization. ... The following*cut*forbids the simultaneous processing of all the transmission*pairs*in EX*t*(k): i∈EXt(k) x i (*t*) < |EX*t*(k)|, ∀*t*= 1, . . . , D (9) These*cuts*should be applied for all*t*for which the ...##
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OPTIMIZATION OF MULTI-PASS FACE MILLING PARAMETERS USING METAHEURISTIC ALGORITHMS

2019
*
Facta Universitatis. Series: Mechanical Engineering
*

Using those algorithms, the

doi:10.22190/fume190605043d
fatcat:6ksdxzi7trgctnoa77n4femr4y
*optimal*values of*cutting*speed, feed rate*and*depth of*cut*for both roughing*and*finishing operations are determined for having*minimum*total production time*and*total production ... Two statistical tests, i.e.*paired**t*-test*and*Wilcoxson signed rank test also confirm its superiority over the remaining algorithms. ... s*t*d d d SInt n (42) where d r min is the*minimum*allowable depth of*cut*for rough passes, d s min is the*minimum*allowable depth of*cut*for finish pass*and*SInt(·) is the smallest integer operator. ...##
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Thresholded Covering Algorithms for Robust and Max-Min Optimization
[article]

2011
*
arXiv
*
pre-print

In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree

arXiv:0912.1045v3
fatcat:3ivx56aqdjfa5hkbocewnbvv3q
*and*set cover,*and*the first approximation algorithms for k-robust Steiner forest,*minimum*-*cut*... The general problem of robust*optimization*is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. ... We thank Chandra Chekuri, Ravishankar Krishnaswamy, Danny Segev,*and*Maxim Sviridenko for invaluable discussions. ...##
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The Number of Solutions Sufficient for Solving a Family of Problems

2005
*
Mathematics of Operations Research
*

We consider several problems-solutions systems,

doi:10.1287/moor.1050.0161
fatcat:vikibdamrvfu5lcf5w7ixzfhmq
*and*for each one, prove the existence of a small set of solutions that contains an*optimal*solution to every problem. ... The families of problems covered here mostly include separation problems, problems on graphs*and*hypergraphs,*and*SAT problems. ... The authors are grateful to Noga Alon for enlightening comments, fruitful discussions,*and*exposing them to relevant literature. ...##
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Fast approximate energy minimization via graph cuts

2001
*
IEEE Transactions on Pattern Analysis and Machine Intelligence
*

We present two algorithms based on graph

doi:10.1109/34.969114
fatcat:omqk3upxireangpjcog3oeqzwy
*cuts*that efficiently find a local*minimum*with respect to two types of large moves, namely expansion moves*and*swap moves. ... Blake [9],*and*Greig et al. [20] analyze the performance of simulated annealing in cases with a known global*minimum*. 4 IEEE TRANSACTIONS ON PATTERN ANALYSIS*AND*MACHINE INTELLIGENCE, VOL. 23, NO. 11, ... This research has been supported by DARPA under contract DAAL01-97-K-0104, by the US National Science Foundation awards CDA-9703470*and*IIS-9900115,*and*by a grant from Microsoft. ...##
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A simple minimum T-cut algorithm

2003
*
Discrete Applied Mathematics
*

We give a simple algorithm for ÿnding a

doi:10.1016/s0166-218x(03)00182-3
fatcat:iw6vus3spbe6jkrrf5sjc3uhwu
*minimum**T*-*cut*. At present, all known e cient algorithms for this problem go through the computation of a Gomory-Hu tree. ... This solution is easier to implement*and*faster to run. Our results extend to the whole of symmetric submodular functions. ? ... Their suggestions*and*advice signiÿcantly helped improving the presentation. ...##
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Fast approximate energy minimization via graph cuts

1999
*
Proceedings of the Seventh IEEE International Conference on Computer Vision
*

We present two algorithms based on graph

doi:10.1109/iccv.1999.791245
dblp:conf/iccv/BoykovVZ99
fatcat:v6i6o2ql4fde7jaymrbrir4ila
*cuts*that efficiently find a local*minimum*with respect to two types of large moves, namely expansion moves*and*swap moves. ... Blake [9],*and*Greig et al. [20] analyze the performance of simulated annealing in cases with a known global*minimum*. 4 IEEE TRANSACTIONS ON PATTERN ANALYSIS*AND*MACHINE INTELLIGENCE, VOL. 23, NO. 11, ... This research has been supported by DARPA under contract DAAL01-97-K-0104, by the US National Science Foundation awards CDA-9703470*and*IIS-9900115,*and*by a grant from Microsoft. ...##
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Flow trees for vertex-capacitated networks

2007
*
Discrete Applied Mathematics
*

Given a graph G = (V , E) with a cost function c(S) 0 ∀S ⊆ V , we want to represent all possible min-

doi:10.1016/j.dam.2006.08.012
fatcat:ginurlyyzzgb7nlwu6qnibzyoq
*cut*values between*pairs*of vertices i*and*j . ... We consider two variants of*cuts*: in the first one, separation, {i}*and*{j } are feasible*cuts*that disconnect i*and*j . ... The ALL-*PAIR**MINIMUM**CUT*PROBLEM is to compute a*minimum*capacity s −*t**cut*for every s,*t*∈ V . If G is a tree, the problem is particularly simple. ...##
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A Parallel Implementation of Gomory-Hu's Cut Tree Algorithm

2012
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2012 IEEE 24th International Symposium on Computer Architecture and High Performance Computing
*

The strategy is optimistic in the sense that the master process manipulates the tree being constructed

doi:10.1109/sbac-pad.2012.37
dblp:conf/sbac-pad/CohenRD12
fatcat:6si2lautizgsnjxhyfl2te4fxi
*and*the slaves solve*minimum*s-*t*-*cuts*independently. ...*Cut*trees are a compact representation of the edge-connectivity between every*pair*of vertices of an undirected graph,*and*have a large number of applications. ...*pairs**minimum*s-*t*-*cut*problem. ...##
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The planar multiterminal cut problem

1998
*
Discrete Applied Mathematics
*

Our main results are two new structural theorems for

doi:10.1016/s0166-218x(98)00036-5
fatcat:tv3ijgmkgbhkxa636m3rlj4qki
*optimal*solutions to the min V-*cut*problem when G is planar. ... The weight of a V'-*cut*is the sum of the weights of its edges. The min V'-*cut*problem is to find a*minimum*weight V'-*cut*. ... Let A be the edges in a*minimum*weight spanning*T*-forest of Gd*and*let B be the edges in a minimal all V'-*pairs*min*cut*collection qf G(E\A). Then{A U B} is a min V/-*cut*. ...##
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Ordered optimal solutions and parametric minimum cut problems

2005
*
Discrete Optimization
*

Based on this result, we present necessary

doi:10.1016/j.disopt.2005.03.002
fatcat:466urqylwrbgdfkcrwnlytmixq
*and*sufficient conditions that ensure the existence of totally ordered selections of*minimum**cuts*for some classes of parametric maximum flow problems. ... In this paper, we present an algebraic sufficient condition for the existence of a selection of*optimal*solutions in a parametric*optimization*problem that are totally ordered, but not necessarily monotone ... The following definitions*and*results help identify sets of arcs related to*minimum**cuts*, across which each*pair*of arcs is parallel. ...
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