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Minimum T-cuts and optimal T-pairings

Romeo Rizzi
2002 Discrete Mathematics  
We introduce the notion of 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 Zoltà an Szigeti and Andrà as Sebő who were among the ÿrst to encourage me on these results.  ... 
doi:10.1016/s0012-365x(02)00397-7 fatcat:wgyvoah4hjbpnfddeodkwsbwoq

On the Robustness of Distributed Computing Networks [article]

Jianan Zhang, Hyang-Won Lee, Eytan Modiano
2021 arXiv   pre-print
We define 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] .  ... 
arXiv:1901.02636v3 fatcat:k5lpbcshw5drfhjrmg3obyulpi

An optimal graph theoretic approach to data clustering: theory and its application to image segmentation

Z. Wu, R. Leahy
1993 IEEE Transactions on Pattern Analysis and Machine Intelligence  
For graphs of moderate size (-2000 vertices), the 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.  ... 
doi:10.1109/34.244673 fatcat:eisqkbw7vbfmhc6wje326zlsga

Parametric min-cuts analysis in a network

Y.P Aneja, R Chandrasekaran, K.P.K Nair
2003 Discrete Applied Mathematics  
The all 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.  ... 
doi:10.1016/s0166-218x(02)00496-1 fatcat:bgx4lxltdrfsfn2cg66vw2umem

Reduced power expenditure in the minimum latency transmission scheduling problem

Kyriakos M. Deliparaschos, Themistoklis Charalambous, Paul Christodoulides, Evelina Klerides
2014 2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP)  
The 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  ... 
doi:10.1109/isccsp.2014.6877851 dblp:conf/isccsp/DeliparaschosCC14 fatcat:idrzlvwi75h3hgj6kmc3iip4eq

OPTIMIZATION OF MULTI-PASS FACE MILLING PARAMETERS USING METAHEURISTIC ALGORITHMS

Sunny Diyaley, Shankar Chakraborty
2019 Facta Universitatis. Series: Mechanical Engineering  
Using those algorithms, the 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.  ... 
doi:10.22190/fume190605043d fatcat:6ksdxzi7trgctnoa77n4femr4y

Thresholded Covering Algorithms for Robust and Max-Min Optimization [article]

Anupam Gupta, Viswanath Nagarajan, R. Ravi
2011 arXiv   pre-print
In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree 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.  ... 
arXiv:0912.1045v3 fatcat:3ivx56aqdjfa5hkbocewnbvv3q

The Number of Solutions Sufficient for Solving a Family of Problems

Ori Einstein, Refael Hassin
2005 Mathematics of Operations Research  
We consider several problems-solutions systems, 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.  ... 
doi:10.1287/moor.1050.0161 fatcat:vikibdamrvfu5lcf5w7ixzfhmq

Fast approximate energy minimization via graph cuts

Y. Boykov, O. Veksler, R. Zabih
2001 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We present two algorithms based on graph 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.  ... 
doi:10.1109/34.969114 fatcat:omqk3upxireangpjcog3oeqzwy

A simple minimum T-cut algorithm

Romeo Rizzi
2003 Discrete Applied Mathematics  
We give a simple algorithm for ÿnding a 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.  ... 
doi:10.1016/s0166-218x(03)00182-3 fatcat:iw6vus3spbe6jkrrf5sjc3uhwu

Fast approximate energy minimization via graph cuts

Y. Boykov, O. Veksler, R. Zabih
1999 Proceedings of the Seventh IEEE International Conference on Computer Vision  
We present two algorithms based on graph 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.  ... 
doi:10.1109/iccv.1999.791245 dblp:conf/iccv/BoykovVZ99 fatcat:v6i6o2ql4fde7jaymrbrir4ila

Flow trees for vertex-capacitated networks

Refael Hassin, Asaf Levin
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-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.  ... 
doi:10.1016/j.dam.2006.08.012 fatcat:ginurlyyzzgb7nlwu6qnibzyoq

A Parallel Implementation of Gomory-Hu's Cut Tree Algorithm

Jaime Cohen, Luiz A. Rodrigues, Elias P. Duarte Jr.
2012 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 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.  ... 
doi:10.1109/sbac-pad.2012.37 dblp:conf/sbac-pad/CohenRD12 fatcat:6si2lautizgsnjxhyfl2te4fxi

The planar multiterminal cut problem

David Hartvigsen
1998 Discrete Applied Mathematics  
Our main results are two new structural theorems for 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.  ... 
doi:10.1016/s0166-218x(98)00036-5 fatcat:tv3ijgmkgbhkxa636m3rlj4qki

Ordered optimal solutions and parametric minimum cut problems

Shelby Brumelle, Daniel Granot, Li Liu
2005 Discrete Optimization  
Based on this result, we present necessary 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.  ... 
doi:10.1016/j.disopt.2005.03.002 fatcat:466urqylwrbgdfkcrwnlytmixq
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