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Perfect Matchings in O(n n) Time in Regular Bipartite Graphs
[article]
2010
arXiv
pre-print
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In this paper we consider the well-studied problem of finding a perfect matching in a d-regular bipartite graph on 2n nodes with m=nd edges. ...
In a recent line of work by Goel, Kapralov and Khanna the O(m) time algorithm was improved first to Õ(minm, n^2.5/d) and then to Õ(minm, n^2/d). ...
Remark 9 Our algorithm can be used to obtain a simple algorithm for edge-coloring bipartite graphs with maximum degree d in time O(m log n) (slightly worse than the best known O(m log d) dependence obtained ...
arXiv:0909.3346v3
fatcat:rh4z6n5dvzbshmwyhl7scsluaq
Perfect matchings in o(nlogn) time in regular bipartite graphs
2010
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
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We also show that there does not exist a randomized algorithm that finds a matching in a regular bipartite multigraph and takes o(n log n) time with high probability. ...
In this paper we consider the well-studied problem of finding a perfect matching in a d-regular bipartite graph on 2n nodes with m = nd edges. ...
Our algorithm can be used to obtain a simple algorithm for edge-coloring bipartite graphs with maximum degree d in time O(m log n) (slightly worse than the best known O(m log d) dependence obtained in ...
doi:10.1145/1806689.1806697
dblp:conf/stoc/GoelKK10
fatcat:wx4wlsgsmvhxliw7otjsezac54
Perfect Matchings in $O(n\log n)$ Time in Regular Bipartite Graphs
2013
SIAM journal on computing (Print)
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We also show that there does not exist a randomized algorithm that finds a matching in a regular bipartite multigraph and takes o(n log n) time with high probability. ...
In this paper we consider the well-studied problem of finding a perfect matching in a d-regular bipartite graph on 2n nodes with m = nd edges. ...
Our algorithm can be used to obtain a simple algorithm for edge-coloring bipartite graphs with maximum degree d in time O(m log n) (slightly worse than the best known O(m log d) dependence obtained in ...
doi:10.1137/100812513
fatcat:2fsrhiuj4jgptou63nhqonxqs4
Node-based scheduling with provable evacuation time
2015
2015 49th Annual Conference on Information Sciences and Systems (CISS)
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In this setting, the minimum evacuation time problem is equivalent to the classic multigraph edge coloring problem, which is generally NP-hard. ...
Instead, it is desirable to compute the schedules (or the colors) in an online fashion, i.e., to quickly compute one schedule at a time. ...
ACKNOWLEDGMENT This work was supported in part by the NSF under Grants CNS-1449860, CNS-1065444, and ECCS-1231461. ...
doi:10.1109/ciss.2015.7086428
dblp:conf/ciss/JiW15
fatcat:w6okgii45bcrhhoohnzstzafdy
Another Simple Algorithm for Edge-Coloring Bipartite Graphs
2005
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
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with m edges and maximum degree d in O(m log d + (m/d) log(m/d)) time. ...
This algorithm, based on the framework of the O(m log d + (m/d) log(m/d) log d) algorithm by Makino-Takabatake-Fujishige and the O(m log m) one by Alon, finds an optimal edge-coloring of a bipartite graph ...
Edge-Sparsification in Step 4 costs O((n log d) log 2 2d ) = O(m log d) time, since H is an xd-regular bipartite multigraph with O(n log d) distinct edges. Step 5 costs O(n) time. ...
doi:10.1093/ietfec/e88-a.5.1303
fatcat:h5bdlai65bgbjixkw4a2ibizjq
Finding the KT partition of a weighted graph in near-linear time
[article]
2021
arXiv
pre-print
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We give a O(m log^4 n) time deterministic algorithm to compute a spanning forest of H. ...
In a breakthrough work, Kawarabayashi and Thorup (J. ACM'19) gave a near-linear time deterministic algorithm for minimum cut in a simple graph G = (V,E). ...
One can use Gabow's deterministic O(λm log n) edge connectivity algorithm [Gab95] for a multigraph with m edges and edge connectivity λ to check in time O(nd log n) = O(m) if the edge connectivity of ...
arXiv:2111.01378v1
fatcat:w3basxih7vactpikdrcwtuqdy4
Node-based Service-Balanced Scheduling for Provably Guaranteed Throughput and Evacuation Time Performance
[article]
2017
arXiv
pre-print
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It is remarkable that NSB is both throughput-optimal and evacuation-time-optimal if the underlying network graph is bipartite. ...
NSB aims to give scheduling opportunities to heavily congested nodes in a balanced manner, by maximizing the total weight of the scheduled nodes in each scheduling cycle, where the weight of a node is ...
Algorithm Complexity γ (Throughput) η (Evacuation time) General Bipartite General Bipartite MWM O(mn) 1 1 2 2 GMM O(m log m) ≥ 1/2 ≥ 1/2 2 2 MM O(m) ≥ 1/2 ≥ 1/2 2 2 MVM O(m √ n log n) ? ...
arXiv:1512.02328v2
fatcat:uz5t5spttzaotfg5eyuah37r6i
Node-Based Service-Balanced Scheduling for Provably Guaranteed Throughput and Evacuation Time Performance
2018
IEEE Transactions on Mobile Computing
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It is remarkable that NSB is both throughput-optimal and evacuation-time-optimal if the underlying network graph is bipartite. ...
In this paper, we adopt a novel node-based approach and propose a service-balanced online scheduling algorithm, called NSB, which gives balanced scheduling opportunities to the nodes with heavy workload ...
Algorithm Complexity γ (Throughput) η (Evacuation time) General Bipartite General Bipartite MWM O(mn) 1 1 2 2 GMM O(m log m) ≥ 1/2 ≥ 1/2 2 2 MM O(m) ≥ 1/2 ≥ 1/2 2 2 MVM O(m √ n log n) unknown 1 ≤ 3/2 1 ...
doi:10.1109/tmc.2017.2777828
fatcat:3wv4k2w7jjgcrm62rahwsii3ji
Node-based service-balanced scheduling for provably guaranteed throughput and evacuation time performance
2016
IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications
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It is remarkable that NSB is both throughput-optimal and evacuation-time-optimal if the underlying network graph is bipartite. ...
In this paper, we adopt a novel node-based approach and propose a service-balanced online scheduling algorithm, called NSB, which gives balanced scheduling opportunities to the nodes with heavy workload ...
Algorithm Complexity γ (Throughput) η (Evacuation time) General Bipartite General Bipartite MWM O(mn) 1 1 2 2 GMM O(m log m) ≥ 1/2 ≥ 1/2 2 2 MM O(m) ≥ 1/2 ≥ 1/2 2 2 MVM O(m √ n log n) unknown 1 ≤ 3/2 1 ...
doi:10.1109/infocom.2016.7524617
dblp:conf/infocom/JiGS16
fatcat:saejdrrpxzf2jcrjz34kc47bfy
Network Coding Gaps for Completion Times of Multiple Unicasts
[article]
2020
arXiv
pre-print
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Our results also hold for average completion time, and more generally any ℓ_p norm of completion times. ...
In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible. ...
Acknowledgements The authors would like to thank Mohsen Ghaffari for suggesting an improvement to Theorem 1.2 which resulted in a coding gap independent of n, Anupam Gupta for pointing out a simplification ...
arXiv:1905.02805v3
fatcat:dq4mgw5s35cntgqubqvwpx2zvq
Dedicated Scheduling of Biprocessor Tasks to Minimize Mean Flow Time
[chapter]
2002
Lecture Notes in Computer Science
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In this way we identify a borderline between NP-hard and polynomially solvable special cases. ...
This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to minimize mean flow time. ...
If G = (V 1 ∪ V 2 , E) is a bipartite graph in which deg(x) ≥ deg (y) for each edge xy with x ∈ V 1 , y ∈ V 2 then an optimal sum coloring can be found in time O(|E|log∆). ...
doi:10.1007/3-540-48086-2_10
fatcat:nzg42exdgnar7lghsahcz4jebi
Edge-coloring algorithms
[chapter]
1995
Lecture Notes in Computer Science
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In this paper, we survey recent advances and results on the classical edge-coloring problem as well as the generalized edge-coloring problems, called the f-coloring and fg-coloring problems. ...
In particular we review various upper bounds on the minimum number of colors required to edge-color graphs, and present efficient algorithms to edge-color graphs with a number of colors not exceeding the ...
There exists a more efficient algorithm which, based on the divide and conquer, edge-colors a bipartite multigraph in time O(m log m) [8] .
with [-~z~(a)J colors in time O(m(A(a) + e)). ...
doi:10.1007/bfb0015243
fatcat:gh5b6z4745fd5i3dd7f5t6gpsm
Computing Quartet Distance is Equivalent to Counting 4-Cycles
[article]
2020
arXiv
pre-print
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2018 pre-print arXiv:1811.06244v1 fatcat:422pn6ibsvhwrj5z6ge7uef6uy
[SODA 2013] presented an algorithm that computes this number in 𝒪(ndlog n) time, where d is the maximum degree of a node. ...
For trees with degrees bounded by d, by analysing the reduction more carefully, we are able to obtain an Õ(nd^0.77) time algorithm, which is again a nontrivial improvement on the previous bound of 𝒪(ndlog ...
In total there are at most 2 nodes of type (1) at each side of the graph. To conclude, we can construct the bipartite multigraph M with O(|L|) non-zero edges in O(|L| log |L|) time. ...
arXiv:1811.06244v2
fatcat:kdd6gz5g6zcfrb6wnjx2ztgpim
Decompositions to Degree-Constrainded Subgraphs Are Simply Reducible to Edge-Colorings
1999
Journal of combinatorial theory. Series B (Print)
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In this paper we show that the problem can be simply reduced to the edge-coloring problem in polynomial-time. ...
be edge-colored with k colors. ...
Thus we have |E(G f k )| : [ |E(P(v))|: v # V] =O \ : v # V d(v)(2 f ) 3 log 2 f 2 + O(|E| (2 f ) 3 log 2 f 2). ...
doi:10.1006/jctb.1998.1883
fatcat:etxdchk3grd4rdty4mznkr33eu
Fully Polynomial-Time Distributed Computation in Low-Treewidth Graphs
2022
Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
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This is the first exact algorithm for the directed single-source shortest paths problem in low-treewidth graphs attaining a Õ (𝜏 𝑂 (1) 𝐷)-round running time. • Exact bipartite unweighted maximum matching ...
can be computed in Õ (𝜏 4 𝐷 + 𝜏 7 ) rounds. ...
The depth of 𝑇 is 𝑂 (log 𝑛) and the running time of the algorithm is Õ (𝜏 2 𝐷 + 𝜏 3 ) rounds. ...
doi:10.1145/3490148.3538590
fatcat:vwfkvxvzufcalg5ghaxf67pksq
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