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Page 5947 of Mathematical Reviews Vol. , Issue 99i [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
{For the entire collection see MR 99e:60008. } 991:05186 05C80 05C0s Haggstrom, Olle (NL-UTRE; Utrecht) Uniform and minimal essential spanning forests on trees.  ...  It is shown by the author that the measures of uniform essential forests and minimal essential forests on trees are differ- ent, but share some basic properties: both are invariant and graph automorphisms  ... 
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Minimal spanning forests

Russell Lyons,, Yuval Peres, Oded Schramm
<span title="">2006</span> <i title="Institute of Mathematical Statistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hwkwbkjkh5esra7lpopyhe65uy" style="color: black;">Annals of Probability</a> </i> &nbsp;
Minimal spanning forests on infinite graphs are weak limits of minimal spanning trees from finite subgraphs.  ...  These limits can be taken with free or wired boundary conditions and are denoted FMSF (free minimal spanning forest) and WMSF (wired minimal spanning forest), respectively.  ...  We thank Itai Benjamini for useful discussions at the early stages of this work, and Gábor Pete for comments on the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/009117906000000269">doi:10.1214/009117906000000269</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fydt3y5qozcipaqdtwcmk5whbu">fatcat:fydt3y5qozcipaqdtwcmk5whbu</a> </span>
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Page 4769 of Mathematical Reviews Vol. , Issue 98H [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Aleksandar Jurisié (Ljubljana) 98h:05065 05C10 05C35 Cole, T. (5-MELB; Parkville) Non-crossing of plane minimal spanning and minimal 7 | networks.  ...  The author proves that for any collection of Euclidean plane points, a minimal length 7; network intersects a minimal spanning tree only at the given Euclidean points. R. S.  ... 
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Ends in free minimal spanning forests

Ádám Timár
<span title="">2006</span> <i title="Institute of Mathematical Statistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hwkwbkjkh5esra7lpopyhe65uy" style="color: black;">Annals of Probability</a> </i> &nbsp;
We show that for a transitive unimodular graph, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of Lyons, Peres and Schramm.  ...  I thank Russell Lyons and Gábor Pete for their comments on the manuscript. 6Á. TIMÁR  ...  Minimal spanning forests of finite graphs have been studied for a long time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/009117906000000025">doi:10.1214/009117906000000025</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wy3wr7ofkjgd5biarrbkxtcll4">fatcat:wy3wr7ofkjgd5biarrbkxtcll4</a> </span>
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Approximation Algorithms for Capacitated Minimum Forest Problems in Wireless Sensor Networks with a Mobile Sink

Weifa Liang, Pascal Schweitzer, Zichuan Xu
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5jlmyrayyrdazh5awdlsoec77q" style="color: black;">IEEE transactions on computers</a> </i> &nbsp;
The proposed algorithms are the first approximation algorithms for the capacitated minimum forest problem, and our techniques may be applicable to other constrained optimization problems beyond wireless  ...  The architecture consists of sensor nodes, gateway nodes and mobile sinks.  ...  Within the minimum spanning forest, each tree is a tree rooted at a gateway node, and there is not any capacity constraints on gateway nodes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tc.2012.124">doi:10.1109/tc.2012.124</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rn7dycybdfcqnkl5uodw42qaai">fatcat:rn7dycybdfcqnkl5uodw42qaai</a> </span>
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Metropolized Forest Recombination for Monte Carlo Sampling of Graph Partitions [article]

Eric Autrey and Daniel Carter and Gregory Herschlag and Zach Hunter and Jonathan C. Mattingly
<span title="2021-05-10">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our proposal chain modifies the recently developed method called Recombination (ReCom), which draws spanning trees on joined partitions and then randomly cuts them to repartition.  ...  We improve the computational efficiency by augmenting the state space from partitions to spanning forests.  ...  We also thank the Rhodes Information Intiative and the Duke Provost and Deans office for financial support and creating a productive working environment.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.01503v2">arXiv:1911.01503v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2grqc24l2jbfhcguhosbrww3pq">fatcat:2grqc24l2jbfhcguhosbrww3pq</a> </span>
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Determinantal spanning forests on planar graphs [article]

Richard Kenyon
<span title="2017-02-13">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite.  ...  Like the uniform spanning tree, these measures arise naturally from the laplacian on the graph.  ...  shows random samples from three other measures on the same graph; these are measures on essential spanning forests (ESFs); an essential spanning forest is a spanning forest each of whose components is  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.03802v1">arXiv:1702.03802v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y3m3jyieqnc3ln3af7an3cix7e">fatcat:y3m3jyieqnc3ln3af7an3cix7e</a> </span>
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Multi-robot forest coverage

Xiaoming Zheng, Sonal Jain, S. Koenig, D. Kempe
<span title="">2005</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dmucnarmarh2fj6syg5jyqs7ny" style="color: black;">2005 IEEE/RSJ International Conference on Intelligent Robots and Systems</a> </i> &nbsp;
In this paper, we describe Multi-Robot Forest Coverage, a new multirobot coverage algorithm based on an algorithm by Even et al. for finding a tree cover with trees of balanced weights.  ...  The cover time of Multi-Robot Forest Coverage is at most eight times larger than optimal, and our experiments show it to perform significantly better than existing multi-robot coverage algorithms.  ...  The single-robot coverage problem is solved essentially optimally by Spanning Tree Coverage (STC), a polynomialtime coverage algorithm that decomposes terrain into cells, computes a spanning tree of the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2005.1545323">doi:10.1109/iros.2005.1545323</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iros/ZhengJKK05.html">dblp:conf/iros/ZhengJKK05</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ryxgvmporfhzzaza7jtkutiap4">fatcat:ryxgvmporfhzzaza7jtkutiap4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809101637/http://www.cpp.edu/~ftang/courses/CS599-DI/notes/papers/iros05.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c9/b3/c9b3699e8843591926178a6c0e78e71d43d6bcfd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/iros.2005.1545323"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Sampling Tree Fragments from Forests

Tagyoung Chung, Licheng Fang, Daniel Gildea, Daniel Štefankovič
<span title="">2014</span> <i title="MIT Press - Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e4yflo6sufcufjwloald7xudm4" style="color: black;">Computational Linguistics</a> </i> &nbsp;
We study the problem of sampling trees from forests, in the setting where probabilities for each tree may be a function of arbitrarily large tree fragments.  ...  We develop a Markov chain Monte Carlo (MCMC) algorithm which corrects for the bias introduced by unbalanced forests, and we present experiments using the algorithm to learn Synchronous Context-Free Grammar  ...  , LDC2003E07, LDC2003E14, LDC2004T08, LDC2005T06, LDC2005T10, LDC2005T34, LDC2006E26, LDC2005E83, LDC2006E34, LDC2006E85, LDC2006E92, LDC2006E24, LDC2006E92, LDC2006E24) The language model is trained on  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/coli_a_00170">doi:10.1162/coli_a_00170</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/slvirjjyjbcrxjm66i3zklv7l4">fatcat:slvirjjyjbcrxjm66i3zklv7l4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808222219/https://www.cs.rochester.edu/~gildea/pubs/chung-cl13.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ec/73/ec73af6567e1b8b26c529491bc90af4efbc18b2f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/coli_a_00170"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mitpressjournals.org </button> </a>

Interlacements and the wired uniform spanning forest

Tom Hutchcroft
<span title="">2018</span> <i title="Institute of Mathematical Statistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hwkwbkjkh5esra7lpopyhe65uy" style="color: black;">Annals of Probability</a> </i> &nbsp;
We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs.  ...  of 'excessive ends' in the WUSF is non-random in any graph, and also that every component of the WUSF is one-ended almost surely in any transient unimodular random rooted graph.  ...  We also thank Tyler Helmuth for his careful reading of an earlier version of this manuscript, and thank both Russ Lyons and the anonymous referee for suggesting many corrections and improvements to the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/17-aop1203">doi:10.1214/17-aop1203</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yemgeoefabgwjnrzbhksj5atpq">fatcat:yemgeoefabgwjnrzbhksj5atpq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190430205522/https://www.repository.cam.ac.uk/bitstream/handle/1810/273433/InterlacementsRevised2AOP.pdf;jsessionid=438C91CC447EABB900BAC15A7A7BCB61?sequence=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/45/a4/45a446aca492644492e372c7a9745f79493ff2ff.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/17-aop1203"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Tree and forest weights and their application to nonuniform random graphs

Brian D. Jones, Boris G. Pittel, Joseph S. Verducci
<span title="">1999</span> <i title="Institute of Mathematical Statistics"> The Annals of Applied Probability </i> &nbsp;
The second author expresses his gratitude to Mark Jerrum, Jeff Kahn and David Wilson for stimulating discussions on random trees and forests during his visit to Dimacs Center (Rutgers University) in the  ...  All three of us are grateful to a referee for a careful reading of the paper and many thoughtful suggestions.  ...  ( 1 -COROLLARY 1 . 11 Ce/n]), is a spanning tree. Let e and P(e) denote the set of all spanning trees on Kn and the probability in question.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/aoap/1029962602">doi:10.1214/aoap/1029962602</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sfo6ojnk4vd35j65bwvnmt344u">fatcat:sfo6ojnk4vd35j65bwvnmt344u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190429061230/https://digital.kenyon.edu/cgi/viewcontent.cgi?article=1026&amp;context=math_pubs" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/81/82/8182c9be26722fe477238f93e03dbf10ad07acbd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1214/aoap/1029962602"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Critical Percolation and the Minimal Spanning Tree in Slabs

Charles Newman, Vincent Tassion, Wei Wu
<span title="2017-08-30">2017</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eruewc6pebchzl4z7eavobckae" style="color: black;">Communications on Pure and Applied Mathematics</a> </i> &nbsp;
Another natural random forest measure on infinite graphs is the uniform spanning forest, defined as the weak limit of uniform spanning trees on finite subgraphs.  ...  The minimal spanning forest on Z d is known to consist of a single tree for d Ä 2 and is conjectured to consist of infinitely many trees for large d .  ...  We thank Artem Sapozhnikov for very helpful comments on earlier versions of the paper and Vladas Sidoravicius for useful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/cpa.21714">doi:10.1002/cpa.21714</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vmd33djbg5bxfced34o6skm46i">fatcat:vmd33djbg5bxfced34o6skm46i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201105081821/http://wrap.warwick.ac.uk/114352/1/WRAP-critical-percolation-minimal-spanning-tree-slabs-Wu-2020.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f7/a8/f7a8d15d6bee73161ec6a8936fe13f8aacc63cee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/cpa.21714"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Navigating Giga-Graphs

James Abello, Jeffrey Korn, Matthias Kreuseler
<span title="">2002</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dykylhbvizgerh5htrk2qq5zti" style="color: black;">Proceedings of the Working Conference on Advanced Visual Interfaces - AVI &#39;02</a> </i> &nbsp;
One is tree-map based and the other is obtained by a special sequence of graph edge contractions.  ...  They are based on the notions of Graph Macro-Views, Graph Sketches and Rectangular FishEye Views.  ...  This spanning forest contains the essential macroconnectivity information of the input graph ¡ .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1556262.1556308">doi:10.1145/1556262.1556308</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/avi/AbelloKK02.html">dblp:conf/avi/AbelloKK02</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wnt7stwvgrgthkr66yujy2orqu">fatcat:wnt7stwvgrgthkr66yujy2orqu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20061213131533/http://www.mgvis.com:80/Papers/Visualization/gigagraphs_avi02.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/e6/bfe61cd960d2499a76c368a64136e39cc124040d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1556262.1556308"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Nonunitarizable Representations and Random Forests

I. Epstein, N. Monod
<span title="2009-06-23">2009</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mjvsxmuxeje55kwqek2yas5f7i" style="color: black;">International mathematics research notices</a> </i> &nbsp;
We establish a connection between Dixmier's unitarisability problem and the expected degree of random forests on a group.  ...  Suppose that G is finite and already endowed with a graph structure (G, E). The uniform measure on the set of all spanning trees of (G, E) is a random forest.  ...  Pemantle [Pem91] showed that the uniform spanning tree measure on g n converges weakly to a measure on F H .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/imrn/rnp090">doi:10.1093/imrn/rnp090</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zpgqo4mjvfgwhaqltgo2a53574">fatcat:zpgqo4mjvfgwhaqltgo2a53574</a> </span>
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Fairest edge usage and minimum expected overlap for random spanning trees [article]

Nathan Albin and Jason Clemens and Derek Hoare and Pietro Poggi-Corradini and Brandon Sit and Sarah Tymochko
<span title="2018-05-25">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Random spanning trees of a graph G are governed by a corresponding probability mass distribution (or "law"), μ, defined on the set of all spanning trees of G.  ...  A key tool in the analysis is the spanning tree modulus, for which there exists an algorithm based on minimum spanning tree algorithms, such as Kruskal's or Prim's.  ...  Acknowledgments The authors are grateful to Professors Marianne Korten and David Yetter at Kansas State University for organizing an exceptional summer undergraduate research program that led to several  ... 
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