Filters








50,800 Hits in 6.1 sec

Computing exact minimum cuts without knowing the graph [article]

Aviad Rubinstein, Tselil Schramm, S. Matthew Weinberg
2019 arXiv   pre-print
We provide algorithms computing an exact minimum s-t cut in G with Õ(n^5/3) queries, and computing an exact global minimum cut of G with only Õ(n) queries (while learning the graph requires Θ̃(n^2) queries  ...  We give query-efficient algorithms for the global min-cut and the s-t cut problem in unweighted, undirected graphs.  ...  Acknowledgements The authors thank Robert Krauthgamer, Satish Rao, Aaron Schild, and anonymous reviewers for helpful conversations and suggestions. References  ... 
arXiv:1711.03165v2 fatcat:f2o5zvipifepxguuoeldzwbjma

Computing Exact Minimum Cuts Without Knowing the Graph

Aviad Rubinstein, Tselil Schramm, S Weinberg
unpublished
We provide algorithms computing an exact minimum s-t cut in G with O(n 5/3) queries, and computing an exact global minimum cut of G with only O(n) queries (while learning the graph requires Θ(n 2) queries  ...  Our goal is to minimize the number of queries to the oracle while computing (exact) optimum cuts.  ...  The authors thank Robert Krauthgamer, Satish Rao, Aaron Schild, and anonymous reviewers for helpful conversations and suggestions.  ... 
fatcat:o26kbbxndzhblgyj27xf7wjlmy

Almost-Tight Distributed Minimum Cut Algorithms [article]

Danupon Nanongkai, Hsin-Hao Su
2014 arXiv   pre-print
To the best of our knowledge, this is the first paper that explicitly studies computing the exact minimum cut in the distributed setting.  ...  We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model).  ...  Computing the exact minimum cut.  ... 
arXiv:1408.0557v1 fatcat:ll75ik6pdjeiljiucqllb6zzqu

Almost-Tight Distributed Minimum Cut Algorithms [chapter]

Danupon Nanongkai, Hsin-Hao Su
2014 Lecture Notes in Computer Science  
To the best of our knowledge, this is the first paper that explicitly studies computing the exact minimum cut in the distributed setting.  ...  We study the problem of computing the minimum cut in a weighted distributed messagepassing networks (the CONGEST model).  ...  Computing the exact minimum cut.  ... 
doi:10.1007/978-3-662-45174-8_30 fatcat:bcrite3xpzd73mxaoadima27gi

Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time

Gramoz Goranci, Monika Henzinger, Mikkel Thorup
2018 ACM Transactions on Algorithms  
maintains a (1 + ε)-approximation to the minimum cut.  ...  We also study space-efficient incremental algorithms for the minimum cut problem.  ...  Combining the above bounds gives the theorem.  ... 
doi:10.1145/3174803 fatcat:e7uzwcw7xngufa5sofkrizokwm

A Faster Exact Separation Algorithm for Blossom Inequalities [chapter]

Adam N. Letchford, Gerhard Reinelt, Dirk Oliver Theis
2004 Lecture Notes in Computer Science  
We propose a new exact separation algorithm for the capacitated case which has the same running time as for the uncapacitated case.  ...  For the sake of brevity, however, we will restrict our introduction to the case of perfect 1-capacitated b-matchings, which includes, for example, the separation problem for perfect 2-matchings.  ...  We need to know how a minimum (φ(e), k e )-cut in G R looks. Suppose that e = {φ(e), j}, i.e., j ∈ V is the other end of the edge e of G.  ... 
doi:10.1007/978-3-540-25960-2_15 fatcat:3m5e7ua7ajaxrpmcdtfwuvg24m

Algorithm Engineering for Cut Problems [article]

Alexander Noe
2021 arXiv   pre-print
This work develops highly-efficient algorithms for the (global) minimum cut problem, the balanced graph partitioning problem and the multiterminal cut problem.  ...  In this work, we aim to partition the vertices of a graph into multiple blocks while minimizing the number of edges that connect different blocks.  ...  We use our exact shared-memory parallel minimum cut algorithm to find the exact minimum cut of the graph.  ... 
arXiv:2108.04566v1 fatcat:4tpyybkhsvg6toiuxkvdvychqu

Intractability of min- and max-cut in streaming graphs

Mariano Zelke
2011 Information Processing Letters  
We show that the exact computation of a minimum or a maximum cut of a given graph G is out of reach for any one-pass streaming algorithm, that is, for any algorithm that runs over the input stream of G's  ...  Therefore, we leave open the natural question on the existence of a multi-pass streaming algorithm that exactly computes a minimum or maximum cut.  ...  Hence, for any one-pass streaming algorithm computing this value without yielding a partition, the proved bound holds as well.  ... 
doi:10.1016/j.ipl.2010.10.017 fatcat:q5ggqazmcrcu5dztyiwv3lpotu

Measuring Uncertainty in Graph Cut Solutions – Efficiently Computing Min-marginal Energies Using Dynamic Graph Cuts [chapter]

Pushmeet Kohli, Philip H. S. Torr
2006 Lecture Notes in Computer Science  
In recent years the use of graph-cuts has become quite popular in computer vision.  ...  We propose a fast and novel algorithm based on dynamic graph cuts to efficiently minimize these energy projections.  ...  as the time taken to compute a single graph cut.  ... 
doi:10.1007/11744047_3 fatcat:ilpokj3iwjbrbktmmnxra4wueq

On the maximum and minimum sizes of a graph with given k-connectivity

Yuefang Sun
2017 Discussiones Mathematicae Graph Theory  
We also compute the exact values and bounds for another parameter f (n, k, t) which is defined as the minimum size of a connected graph G with order n and κ k (G) = t, where 1 ≤ t ≤ n − k and k ≥ 3.  ...  Based on this result, we get the exact values for the maximum size, denoted by g(n, k, t), of a connected graph G with order n and κ k (G) = t.  ...  We would like to thank the anonymous referee for helpful comments and suggestions which indeed help us greatly to improve the quality of our paper.  ... 
doi:10.7151/dmgt.1941 fatcat:xvniw2x2xjbv5jjprqtc22fiha

Recent Advances in Practical Data Reduction [article]

Faisal Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, Darren Strash
2020 arXiv   pre-print
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems.  ...  Moreover, we describe concrete techniques that may be useful for future implementations in the area and give open problems and research questions.  ...  Then any spanning tree must contain at least one edge of each of the minimum cuts. Hence, after computing a spanning tree, every remaining edge can be contracted without losing the minimum cut.  ... 
arXiv:2012.12594v3 fatcat:vpsucno5cvgotovfiihkyyytba

Measuring uncertainty in graph cut solutions

Pushmeet Kohli, Philip H.S. Torr
2008 Computer Vision and Image Understanding  
In this context the question arises as to whether it might be possible to compute a measure of uncertainty associated with the graph-cut solutions.  ...  graph cuts.  ...  This work was supported by the epsrc research grant GR/T21790/01(P) and the ist Programme of the European Community, under the PASCAL Network of Excellence, ist-2002-506778.  ... 
doi:10.1016/j.cviu.2008.07.002 fatcat:5zrk5bb7qbav7auvklk5ljkgna

Symmetric Linear Programming Formulations for Minimum Cut with Applications to TSP [article]

Robert D. Carr, Jennifer Iglesias, Giuseppe Lanciac, Benjamin Moseley
2020 arXiv   pre-print
We introduce multiple symmetric LP relaxations for minimum cut problems. The relaxations give optimal and approximate solutions when the input is a Hamiltonian cycle.  ...  In addition, the LP relaxation of min-cut investigated in this paper has interesting constraints; the LP contains only a single typical min-cut constraint and all other constraints are typically only used  ...  One would want to find an LP formulation that is exact for computing a minimum cut when the graph is a Hamiltonian cycle, but simultaneously as loose as possible for computing the minimum cut for any other  ... 
arXiv:2005.11912v1 fatcat:fqkaqhciwnfwng7lj7r45fvgtu

Shared-memory Exact Minimum Cuts [article]

Monika Henzinger, Alexander Noe, Christian Schulz
2018 arXiv   pre-print
minimum cut is maintained in the contracted graph.  ...  Overall, we arrive at a system that outperforms the fastest state-of-the-art solvers for the exact minimum cut problem significantly.  ...  Conclusion We presented a shared-memory parallel exact algorithm for the minimum cut problem. Our algorithm is based on the algorithms of Nagamochi et al. [24, 25] and of Henzinger et al. [13] .  ... 
arXiv:1808.05458v1 fatcat:zjju4qdfn5d3df7tmmamnutsve

Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs

András A. Benczúr, David R. Karger
2015 SIAM journal on computing (Print)  
Results can be even worse in weighted graphs, where the ratio of total edge weight to minimum cut value is unbounded.  ...  In this new graph, for example, we can run the Ç´Ñ ¿ ¾ µ-time maximum flow algorithm of Goldberg and Rao to find an ×-Ø minimum cut in Ç´Ò ¿ ¾ µ time.  ...  Similarly, an ×-Ø minimum cut of the sampled graph is a´½ ·¯µ-times minimum ×-Ø cut of the original graph.  ... 
doi:10.1137/070705970 fatcat:ulpttmmg6na7xdksgl6sm635o4
« Previous Showing results 1 — 15 out of 50,800 results