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Finding minimum congestion spanning trees

Renato Werneck, João Setubal, Arlindo da Conceicão
2000 ACM Journal of Experimental Algorithmics  
doi:10.1145/351827.384253 fatcat:s7rvdo3w4vdk3f2iudfwaajslu

Minimum congestion spanning trees in planar graphs [article]

M.I. Ostrovskii
2009 arXiv   pre-print
This approach is used to evaluate the spanning tree congestion of triangular grids.  ...  The main purpose of the paper is to develop an approach to evaluation or estimation of the spanning tree congestion of planar graphs.  ...  It is clear that for applications it is interesting to find a spanning tree which minimizes the congestion.  ... 
arXiv:0909.3903v1 fatcat:hq5fn4fugzgvpb7dqrzjscnxk4

Minimum congestion spanning trees in planar graphs

M.I. Ostrovskii
2010 Discrete Mathematics  
This approach is used to evaluate the spanning tree congestion of triangular grids.  ...  The main purpose of the paper is to develop an approach to the evaluation or the estimation of the spanning tree congestion of planar graphs.  ...  It is clear that for applications it is interesting to find a spanning tree which minimizes the congestion.  ... 
doi:10.1016/j.disc.2009.11.016 fatcat:xres54qjobgftocaoxffqdckyq

Minimum congestion spanning trees in bipartite and random graphs

M.I. Ostrovskii
2011 Acta Mathematica Scientia  
It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n 3 2 .  ...  The first problem considered in this paper: is it possible to find upper estimates for the spanning tree congestion for bipartite graphs which are better than for general graphs?  ...  An additional motivation for this study is that minimum congestion spanning trees can be considered as 'congestional' analogues of the well-known shortest (or minimal) spanning trees.  ... 
doi:10.1016/s0252-9602(11)60263-4 fatcat:kv3eldw6uzbvnj5lyf6qjn3w4i

Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication

Ali Mashreghi, Valerie King, Michael Wagner
2019 International Symposium on Distributed Computing  
Building a spanning tree, minimum spanning tree (MST), and BFS tree in a distributed network are fundamental problems which are still not fully understood in terms of time and communication cost.  ...  The first work to succeed in computing a spanning tree with communication sublinear in the number of edges in an asynchronous CONGEST network appeared in DISC 2018.  ...  Computing the spanning tree and the minimum spanning tree (MST) are problems of fundamental importance in distributed computing.  ... 
doi:10.4230/lipics.disc.2019.49 dblp:conf/wdag/MashreghiK19 fatcat:px6lpyu7prc23p3niweh6qqrda

Spanning tree congestion of planar graphs

Hiu Law, Siu Leung, Mikhail Ostrovskii
2014 Involve. A Journal of Mathematics  
of the spanning tree congestion.  ...  Math. 310 (2010), no. 6-7, 1204-1209] can be very far from the value of the spanning tree congestion. (3) We find some more examples in which the congestion indicator can be used to find the exact value  ...  It is clear that for applications it is interesting to find a spanning tree which minimizes the congestion.  ... 
doi:10.2140/involve.2014.7.205 fatcat:pp46n6tcyjb43bxvmn4ntnhvku

Spanning Tree Transformation Of Connected Graphs Into Single-Row Networks

S.L. Loh, S. Salleh, N.H. Sarmin
2010 Zenodo  
Paths are produced by Path-Growing and they are combined into a spanning tree by Tree-Forming.  ...  In this paper, a model for spanning tree transformation of connected graphs into single-row networks, namely Spanning Tree of Connected Graph Modeling (STCGM) will be introduced.  ...  Spanning tree n SP with minimum value of max D minimizes the total energy value and congestion as well as doglegs in single-row network.  ... 
doi:10.5281/zenodo.1332106 fatcat:cbyjsmqsnvhi5l3ieqq6r2bpby

Page 648 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
The minimum congestion over all embeddings into binary trees is called the congestion of G (cng(G)) and the minimum dilation is called the dilation of G (dil(G)).  ...  This paper concerns graphs which have a homeomorphically ir- reducible spanning tree (HIST), that is, a spanning tree with no vertices of degree two.  ... 

Interchanging distance and capacity in probabilistic mappings [article]

Reid Andersen, Uriel Feige
2009 arXiv   pre-print
Harald Racke [STOC 2008] described a new method to obtain hierarchical decompositions of networks in a way that minimizes the congestion.  ...  Racke's approach is based on an equivalence that he discovered between minimizing congestion and minimizing stretch (in a certain setting).  ...  Find a probabilistic mapping into spanning trees with congestion at most δ. (By the discussion above this step takes polynomial time, and δ can be taken to beÕ(log n).  ... 
arXiv:0907.3631v1 fatcat:5cqwe2gkw5b5bnh6ldlfbrgqhq

Minimum congestion spanning trees of grids and discrete toruses

A. Castejón, Mikhail Ostrovskii
2009 Discussiones Mathematicae Graph Theory  
The paper is devoted to estimates of the spanning tree congestion for grid graphs and discrete toruses of dimensions two and three.  ...  It is clear that for applications it is interesting to find a spanning tree which minimizes the congestion.  ...  An additional motivation for this study is that minimum congestion spanning trees can be considered as 'congestional' analogues of the well-known shortest (or minimal) spanning trees.  ... 
doi:10.7151/dmgt.1461 fatcat:5rx42o76hvfy3myxhnkvjud4oy

Low-Congestion Shortcuts without Embedding

Bernhard Haeupler, Taisuke Izumi, Goran Zuzic
2016 Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing - PODC '16  
In this work, we side-step this problem by defining a restricted and more structured form of shortcuts and giving a novel construction algorithm which efficiently finds a shortcut which is, up to a logarithmic  ...  On the positive side, this work also introduced low-congestion shortcuts as an elegant solution to circumvent this problem in certain topologies of interest.  ...  For example, Ghaffari and Haeupler show in [7] that one can solve the Minimum Spanning Tree and Min-Cut problems in O((congestion + dilation) log O(1) n), given an efficient algorithm for finding shortcuts  ... 
doi:10.1145/2933057.2933112 dblp:conf/podc/HaeuplerIZ16 fatcat:yyzfj4yzoja35iyd2cpw4yela4

A distributed algorithm for directed minimum-weight spanning tree

Orr Fischer, Rotem Oshman
2021 Distributed computing  
In the directed minimum spanning tree problem (DMST, also called minimum weight arborescence), the network is given a root node r, and needs to construct a minimum-weight directed spanning tree, rooted  ...  (e.g [14, 26, 15, 8, 9, 22, 17, A Distributed Algorithm for Directed Minimum-Weight Spanning Tree 23, 10]).  ...  We handle this using centers, just as we did in Section 5.2: if the path is short, we can find it by doing a short BFS; and if the path is long, it will contain at least one vertex, and we can use the  ... 
doi:10.1007/s00446-021-00398-3 fatcat:4ozf6vhe3fcbnl43mzsr32i4im

On spanning tree congestion of graphs

Kyohei Kozawa, Yota Otachi, Koichi Yamazaki
2009 Discrete Mathematics  
The edge congestion of G in T is the maximum congestion over all edges in T . The spanning tree congestion of G is the minimum congestion of G in its spanning trees.  ...  We also address lower bounds of spanning tree congestion for the multi-dimensional grids and the hypercubes.  ...  The problem is to find a minimum congestion tree T of G such that E(T ) ⊆ E .  ... 
doi:10.1016/j.disc.2008.12.021 fatcat:rstajzdu7bh7rldhe7ruaxuaqu

Spanning Tree Congestion and Computation of Generalized Győri-Lovász Partition [article]

L. Sunil Chandran and Yun Kuen Cheung and Davis Issac
2018 arXiv   pre-print
We study a natural problem in graph sparsification, the Spanning Tree Congestion () problem. Informally, the problem seeks a spanning tree with no tree-edge routing too many of the original edges.  ...  We present a polynomial-time algorithm which computes a spanning tree with congestion O(√(mn)· n).  ...  The STC problem is to find a spanning tree of minimum congestion. [30] 3. Tree Spanner Problem is to find a spanning tree of minimum dilation.  ... 
arXiv:1802.07632v2 fatcat:tlexezq525ajtmbmglhkqou5wu

Near-Optimal Distributed Maximum Flow

Mohsen Ghaffari, Andreas Karrenbauer, Fabian Kuhn, Christoph Lenzen, Boaz Patt-Shamir
2018 SIAM journal on computing (Print)  
The development of the algorithm contains two results of independent interest: (i) A (D + √ n) · n o(1) -round distributed construction of a spanning tree of average stretch n o(1) .  ...  (ii) A (D + √ n) · n o(1) -round distributed construction of an n o(1) -congestion approximator consisting of the cuts induced by O(log n) virtual trees.  ...  A maximum weight spanning tree T can be computed inÕ(D + √ n) rounds using the minimum weight spanning tree algorithm of Kutten and Peleg [?] .  ... 
doi:10.1137/17m113277x fatcat:jnibestbp5hzhlxxdlsukzh4ym
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