Filters








778 Hits in 6.4 sec

Augmenting Undirected Edge Connectivity in Õ(n2) Time

András A Benczúr, David R Karger
2000 Journal of Algorithms  
We give improved randomized (Monte Carlo) algorithms for 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 ).  ... 
doi:10.1006/jagm.2000.1093 fatcat:rl7xry4pbfeehpyjy6kwi6ljuq

Approximating s-t minimum cuts in Õ(n2) time

András A. Benczúr, David R. Karger
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.  ... 
doi:10.1145/237814.237827 dblp:conf/stoc/BenczurK96 fatcat:i5lmywmb4rbodcftotnn6bznvq

An Õ(n2) algorithm for minimum cuts

David R. Karger, Clifford Stein
1993 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93  
We show that the minimum cut problem for weighted 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.  ... 
doi:10.1145/167088.167281 dblp:conf/stoc/KargerS93 fatcat:qvxuxlalbnhbdhh4g2bojq6guy

An O(n2(m + n log n) log n) min-cost flow algorithm

Zvi Galil, Eva Tardos
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  ... 
doi:10.1109/sfcs.1986.7 dblp:conf/focs/GalilT86 fatcat:p2kx3ty64rflxfnhtlvta6vbz4

Nearly Optimal Time Bounds for kPath in Hypergraphs [article]

Lior Kamma, Ohad Trabelsi
2019 arXiv   pre-print
The fastest algorithms known for kPath run 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 .  ... 
arXiv:1803.04940v2 fatcat:cxx6ro7hvzbeba3wmr4i2p6bgq

Finding maximum flows in undirected graphs seems easier than bipartite matching

David R. Karger, Matthew S. Levine
1998 Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98  
Consider an rr-vertex, m-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.  ... 
doi:10.1145/276698.276714 dblp:conf/stoc/KargerL98 fatcat:vnbqyrtkjngs3gpv6ppc5a6mtm

Recognizing interval digraphs and interval bigraphs in polynomial time

Haiko Müller
1997 Discrete Applied Mathematics  
We give a dynamic programming algorithm recognizing interval bigraphs (interval digraphs) 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.  ... 
doi:10.1016/s0166-218x(97)00027-9 fatcat:ehcy4246cveibd7b2ji7ftdzeq

Finding the most vital edges with respect to the number of spanning trees

Fu-Shang P. Tsen, Ting-Yi Sung, Men-Yang Lin, Lih-Hsing Hsu, W. Myrvold
1994 IEEE Transactions on Reliability  
currently 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.  ... 
doi:10.1109/24.370220 fatcat:qon7rqcj45dv3dkvlzmqkg6p2u

Efficient algorithms for qualitative reasoning about time

Alfonso Gerevini, Lenhart Schubert
1995 Artificial Intelligence  
The approach is an extension of the 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".  ... 
doi:10.1016/0004-3702(94)00016-t fatcat:xoqk6bpgzree3pmlun73etbapq

RECENT DEVELOPMENTS IN MAXIMUM FLOW ALGORITHMS

Takao Asano, Yasuhito Asano
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 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.  ... 
doi:10.15807/jorsj.43.2 fatcat:cvaf6u4v45gkdmwlgems7ewbbi

Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation [article]

Jitendra K Tugnait
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.  ... 
arXiv:2205.00007v1 fatcat:btl6x4i33zfktkqev6upgjex2a

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

Daniel A. Spielman, Shang-Hua Teng
2008 arXiv   pre-print
Vaidya proved that by 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.  ... 
arXiv:cs/0310051v10 fatcat:kct4ghaianctdeebxx3pza5w3e

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).  ... 

A polynomial time algorithm for finding the prime factors of cartesian-product graphs

Joan Feigenbaum, John Hershberger, Alejandro A. Schäffer
1985 Discrete Applied Mathematics  
Then we give a polynomial-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  ... 
doi:10.1016/0166-218x(85)90066-6 fatcat:tklbxjlumve33eocpsgcoljhmq

Minimizing Costs of Resource Requirements in Project Networks Subject to a Fixed Completion Time

Rolf H. Möhring
1984 Operations Research  
On the other hand, carrying out activities simultaneously 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.  ... 
doi:10.1287/opre.32.1.89 fatcat:h7wkcbbj4bejljnnd3fnnxvo7u
« Previous Showing results 1 — 15 out of 778 results