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Augmenting Undirected Edge Connectivity in Õ(n2) Time

2000
*
Journal of Algorithms
*

We give improved randomized (Monte Carlo) algorithms for

doi:10.1006/jagm.2000.1093
fatcat:rl7xry4pbfeehpyjy6kwi6ljuq
*undirected**edge*splitting and*edge**connectivity**augmentation*problems. ... At present, Monte Carlo algorithms are the only way even to test whether a graph is k-*connected**in**o*(nm)*time*[KS96, Kar96] . ... Thus if our algorithm outputs each pane*in**time*proportional to its size, the overall*time*to generate the panes will be*O*(n 2 ). ...##
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Approximating s-t minimum cuts in Õ(n2) time

1996
*
Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96
*

*In*this new graph, for example, we can run the

*Õ*(mn)-

*time*maximum flow algorithm of Goldberg and Tarjan to find an s-t minimum cut

*in*

*Õ*(n 2 )

*time*. ... This corresponds to a (1 + )-

*times*minimum s-t cut

*in*the original graph.

*In*a similar way, we can approximate a sparsest cut

*in*

*Õ*(n 2 )

*time*. ... Corollary 1. 4

*In*an

*undirected*graph, a (1 + )

*times*minimum s-t cut of value v can be found

*in*

*Õ*(nv= 2 )

*time*. ...

##
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An Õ(n2) algorithm for minimum cuts

1993
*
Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93
*

We show that the minimum cut problem for weighted

doi:10.1145/167088.167281
dblp:conf/stoc/KargerS93
fatcat:qvxuxlalbnhbdhh4g2bojq6guy
*undirected*graphs can be solved*in*N C using three separate and independently interesting results. ... We believe that the set-isolation approach will prove useful*in*other derandomization problems. ...*In**O*(m + n log n)*time*they nd a sparse*connectivity*certi cate (i.e., a subgraph that contains all the min-cut*edges*) that excludes some*edge*of the graph. ...##
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An O(n2(m + n log n) log n) min-cost flow algorithm

1986
*
27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
*

*In*this paper we design an

*O*( n 2 ( m + n log n) log n) algorithm. The previous best algorithm had an

*O*( m 2 ( m+n log n) log n)

*time*bound. ... and ~lSRI, Berkeley 1 A preliminary version of the paper appeared

*in*Z. Galil and E. Tardos, An

*O*(n 2 (m + n log n) logn) min-cost flow algorithm. ... I Running

*time*Given P(f, g, d) , let F(f, g, d) = IE(f)1 + IE(g)1 + [comp(Eoo(f, g))]2 where comp(Ed, for a subset of

*edges*E 1 , is the number of

*connected*components

*in*the underlying

*undirected*...

##
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Nearly Optimal Time Bounds for kPath in Hypergraphs
[article]

2019
*
arXiv
*
pre-print

The fastest algorithms known for kPath run

arXiv:1803.04940v2
fatcat:cxx6ro7hvzbeba3wmr4i2p6bgq
*in**time*2^k poly(n) for directed graphs (Williams, 2009), and*in**time*1.66^k poly(n) for*undirected*graphs (Björklund , 2014). ... Specifically, it implies that Set Cover on n elements can be solved*in**time**O*^*(2^(1 - δ)n) for some δ>0. ... Therefore the total*time*required to solve all instances is at most*n2*2t •*O*m ′c • 2 (1−γ)n ′ ≤*O**n2*2 4 √ δn • m c 2 cδn • 2 (1−γ)(1+ 4 √ δ)n =*O** 2 (2 4 √ δ+cδ+(1−γ)(1+ 4 √ δ))n . ...##
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Finding maximum flows in undirected graphs seems easier than bipartite matching

1998
*
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
*

Consider an rr-vertex, m-

doi:10.1145/276698.276714
dblp:conf/stoc/KargerL98
fatcat:vnbqyrtkjngs3gpv6ppc5a6mtm
*edge*,*undirected*graph with maximum llow value v. We give a method to find*augmenting*paths*in*such a graph*in*amortized sub-linear (*O*(n@)*time*per path. ... -For simple graphs,*in*which v s II, the last bound is a(n2s2), improving on the best previous bound of*O*(*n2**5), which is also the best known*time*bound for bipartite matching. ... Acknowledgments We thank Allen Knutson and Joel Rosenberg for assistance*in*proving Theorem 7.1. ...##
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Recognizing interval digraphs and interval bigraphs in polynomial time

1997
*
Discrete Applied Mathematics
*

We give a dynamic programming algorithm recognizing interval bigraphs (interval digraphs)

doi:10.1016/s0166-218x(97)00027-9
fatcat:ehcy4246cveibd7b2ji7ftdzeq
*in*polynomial*time*. ... An interval bigraph is an*undirected*bipartite graph whose*edge*set is the intersection of the*edge*sets of an interval graph and the*edge*set of a complete bipartite graph on the same vertex set. ... Let T, be shorthand for ~~~~ (tj +*Connected*chordal bipartite graphs with n vertices and m*edges*can be recognized*in**time**O*(nm) or even*in**time**O*(min(m logqn"))[15, 191. ...##
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Finding the most vital edges with respect to the number of spanning trees

1994
*
IEEE Transactions on Reliability
*

currently

doi:10.1109/24.370220
fatcat:qon7rqcj45dv3dkvlzmqkg6p2u
*O*(*n2*... We present an algorithm for determining the most vital*edges*based on Kirchoff's matrixtree theorem whose asymptotic*time*-complexity can be reduced to that of the fastest matrix multiplication routine, ... All the*edges*can be processed, as*in*step 2,*in**O*(*n2*)*time*. n u s , the limiting factor is the complexity of matrix multiplication. ...##
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Efficient algorithms for qualitative reasoning about time

1995
*
Artificial Intelligence
*

The approach is an extension of the

doi:10.1016/0004-3702(94)00016-t
fatcat:xoqk6bpgzree3pmlun73etbapq
*time*representation proposed by Schubert, Taugher and Miller*in*the context of story comprehension. ... The algorithms herein enable construction of a timegraph from a given set of PArelations, querying a timegraph, and efficiently checking the consistency of a timegraph*augmented*by a set of PA-disjunctions ... ) , and*in*part at IRST*in*the context of the MAIA project and the CNR projects "Sistemi Informatici e Calcolo Parallelo", and "Pianificazione Automatica". ...##
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RECENT DEVELOPMENTS IN MAXIMUM FLOW ALGORITHMS

2000
*
Journal of the Operations Research Society of Japan
*

Among them are included two new algorithms: the Goldberg-Rao algorithm which finds a maximum fiow on an integral capacity network N of n vertices amd m

doi:10.15807/jorsj.43.2
fatcat:cvaf6u4v45gkdmwlgems7ewbbi
*edges**in**O*(min{mi/2,*n2*/3}m log(*n2*/m) log U) tinie ...*In*this paper, we survey properties of the distance function defined by a length function and give am overvieur on the representative maxirmim fiow algorithrms proposed so far*in*asysternatic way by utilizing ... Each*augmentation*can be done by finding a path from s to t*in**O*(m)*time*and we can obtain fZ on Ni*in**O*(m2)*time*. Thus, a maximum flow*in*IV can be obtained*in**O*(m2logU)*time*. ...##
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Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation
[article]

2022
*
arXiv
*
pre-print

*In*a

*time*series graph, each component of the vector series is represented by distinct node, and associations between components are represented by

*edges*between the corresponding nodes. ... Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches

*in*correctly detecting the graph

*edges*. ... This set-up leads to approximately 3.5%

*connected*

*edges*. The true

*edge*set E0 for the

*time*series graph is determined as follows. ...

##
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Nearly-Linear Time Algorithms for Graph Partitioning, Graph Sparsification, and Solving Linear Systems
[article]

2008
*
arXiv
*
pre-print

Vaidya proved that by

arXiv:cs/0310051v10
fatcat:kct4ghaianctdeebxx3pza5w3e
*augmenting*spanning trees with a few*edges*, one could find*ǫ*-approximate solutions to SDD linear systems of maximum valence d*in**time**O*((dn) 1.75 log(κ f (A)/*ǫ*)), and of planar linear ... +*n2**O*( √ log log log n) . ... Thus, for 1 ≤ i ≤ r, A i will have at most n 1−i/r*edges*. ...##
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Page 3710 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

Based on these facts an algorithm is given to compute an optimal solution of the above

*augmentation*problems*in**time**O*(n*) for any fixed k. ... The (simplicity-preserving) k-*edge*-*connectivity**augmentation*prob- lem is to find a smallest set F of new*edges*whose addition makes the graph k-*edge*-*connected*(without introducing parallel*edges*). ...##
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A polynomial time algorithm for finding the prime factors of cartesian-product graphs

1985
*
Discrete Applied Mathematics
*

Then we give a polynomial-

doi:10.1016/0166-218x(85)90066-6
fatcat:tklbxjlumve33eocpsgcoljhmq
*time*algorithm to compute the relations and to construct the prime factors of any*connected*graph. ... He uses a tower of successively coarser equivalence relations on the*edge*set*in*which each prime factor of the graph is identified with an equivalence class*in*the coarsest of the relations. ... Coincident with the preparation of this manuscript, Peter Winkler developed an*O*(n 4) algorithm for cartesian factoring that does not rely on Sabidussi's work [8] ; Winkler's approach is based on recent ...##
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Minimizing Costs of Resource Requirements in Project Networks Subject to a Fixed Completion Time

1984
*
Operations Research
*

On the other hand, carrying out activities simultaneously

doi:10.1287/opre.32.1.89
fatcat:h7wkcbbj4bejljnnd3fnnxvo7u
*in*order to save*time*will usually result*in*higher costs for the resources consumed. ... are independent of*time*. ... ACKNOWLEDGMENTS This work was supported*in*part by the Minister fur Wissenschaft und Forschung des Landes Nordrhein-Westfalen. ...
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