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A minimum spanning tree algorithm with inverse-Ackermann type complexity

Bernard Chazelle
<span title="2000-11-01">2000</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r72grtxx6jad5hjzl7fxcunwhi" style="color: black;">Journal of the ACM</a> </i> &nbsp;
A faster deterministic algorithm for minimum spanning trees. In  ...  A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented.  ...  We recurse within what is left of the C z 's to produce a spanning forest F. Finally, we throw back in the bad edges and recurse again to produce the minimum spanning tree of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/355541.355562">doi:10.1145/355541.355562</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5busethsfbhxvczhyn6n55qgvm">fatcat:5busethsfbhxvczhyn6n55qgvm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812203643/http://www.cs.princeton.edu/courses/archive/fall05/cos528/handouts/A%20Minimum%20Spanning.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/71/ce/71ce98cbb01319b2796a1fd6e2deb124df0cc975.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/355541.355562"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Sensitivity Analysis of Minimum Spanning Trees in Sub-Inverse-Ackermann Time

Seth Pettie
<span title="">2015</span> <i title="Journal of Graph Algorithms and Applications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4joumle7hffilk276fkubvhxcq" style="color: black;">Journal of Graph Algorithms and Applications</a> </i> &nbsp;
We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(m log α(m, n)) time, where α is the inverse-Ackermann function.  ...  As far as we are aware, our split-findmin algorithm is the first with superlinear but sub-inverse-Ackermann complexity. We also give a reduction from MST sensitivity to the MST problem itself.  ...  Theorem 1 The sensitivity of a minimum spanning tree or single-source shortest path tree can be computed in O(m log α(m, n)) time, where m is the number of edges, n the number of vertices, and α the inverse-Ackermann  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00365">doi:10.7155/jgaa.00365</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wnm235bunjfwdddo5jvvzw43wm">fatcat:wnm235bunjfwdddo5jvvzw43wm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160508205535/http://web.eecs.umich.edu:80/~pettie/papers/sf-JGAA.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/65/2b/652bc5c8f3fc0197c2f8cfb4df6059b744fa941f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.7155/jgaa.00365"> <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>

Sensitivity Analysis of Minimum Spanning Trees in Sub-Inverse-Ackermann Time [article]

Seth Pettie
<span title="2014-07-08">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(mα(m,n)) time, where α is the inverse-Ackermann function.  ...  As far as we are aware, our split-findmin algorithm is the first with superlinear but sub-inverse-Ackermann complexity. We also give a reduction from MST sensitivity to the MST problem itself.  ...  minimum spanning tree or single-source shortest path tree can be computed in O(m log α(m, n)) time, where m is the number of edges, n the number of vertices, and α the inverse-Ackermann function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.1910v1">arXiv:1407.1910v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6lvaiyot2fgljhpzu7lwgxpzx4">fatcat:6lvaiyot2fgljhpzu7lwgxpzx4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191024164227/https://arxiv.org/pdf/1407.1910v1.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/c2/10/c2102c001f93693ac96b7489945fe95cf1eb143c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.1910v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Sensitivity Analysis of Minimum Spanning Trees in Sub-inverse-Ackermann Time [chapter]

Seth Pettie
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a deterministic algorithm for computing the sensitivity of a minimum spanning tree (MST) or shortest path tree in O(m log α(m, n)) time, where α is the inverse-Ackermann function.  ...  As far as we are aware, our split-findmin algorithm is the first with superlinear but sub-inverse-Ackermann complexity. We also give a reduction from MST sensitivity to the MST problem itself.  ...  Theorem 1 The sensitivity of a minimum spanning tree or single-source shortest path tree can be computed in O(m log α(m, n)) time, where m is the number of edges, n the number of vertices, and α the inverse-Ackermann  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11602613_96">doi:10.1007/11602613_96</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7nnugmbvdfbxzobwtwkb3wo3ju">fatcat:7nnugmbvdfbxzobwtwkb3wo3ju</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160508205535/http://web.eecs.umich.edu:80/~pettie/papers/sf-JGAA.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/65/2b/652bc5c8f3fc0197c2f8cfb4df6059b744fa941f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11602613_96"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

An Inverse-Ackermann Type Lower Bound For Online Minimum Spanning Tree Verification*

Seth Pettie†
<span title="">2006</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ujm6quky2va7pmzbitmgsrksbu" style="color: black;">Combinatorica</a> </i> &nbsp;
Given a spanning tree T of some graph G, the problem of minimum spanning tree verification is to decide whether T = MST (G).  ...  It is this application that has led some to wonder whether a more flexible version of MST verification could be used to derive a faster deterministic minimum spanning tree algorithm.  ...  Compare this with the inverse-Ackermann type lower bounds of [39, 4, 11] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00493-006-0014-1">doi:10.1007/s00493-006-0014-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nn4dulz6bbhgjc72tmcn4zgsbm">fatcat:nn4dulz6bbhgjc72tmcn4zgsbm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150908055249/http://web.eecs.umich.edu/~pettie/papers/mst-verification.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/c3/c1/c3c17b7a9b56253937b45b5adbacc798964557e2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00493-006-0014-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 7545 of Mathematical Reviews Vol. , Issue 2002J [page]

<span title="">2002</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;
tree algorithm with inverse-Ackermann type complexity.  ...  Specifically an ap- proximate priority queue, called a soft heap, is used to construct a good, but not necessarily minimum, spanning tree.  ... 
<span class="external-identifiers"> </span>
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Guest Editorial: Computing and Combinatorics

My T. Thai
<span title="2012-04-13">2012</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
The "Shorthand Universal Cycles for Permutations" paper investigates SP-cycles with maximum and minimum 'weight'.  ...  Ackermann function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-012-9649-z">doi:10.1007/s00453-012-9649-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xngsyup6jvdupc7kpwudfivmme">fatcat:xngsyup6jvdupc7kpwudfivmme</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180726135626/https://link.springer.com/content/pdf/10.1007%2Fs00453-012-9649-z.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/0d/41/0d4187550761800d20b02289c3e294a43403cde0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-012-9649-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Distributed Approximation Algorithms for the Combinatorial Motion Planning Problem [article]

Simran Dokania, Aditya Paliwal, Shrisha Rao
<span title="2018-05-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a new 4-approximation algorithm for the Combinatorial Motion Planning problem which runs in O(n^2α(n^2,n)) time, where α is the functional inverse of the Ackermann function, and a fully distributed  ...  version for the same in asynchronous message passing systems, which runs in O(n_2n) time with a message complexity of O(n^2).  ...  Specifically, Hoogeven shows that for a graph G = (V, E) with a minimum spanning tree M ST , a minimum cost perfect matching M over all the vertices with odd degree in the spanning tree, an optimal Hamiltonian  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1805.08978v1">arXiv:1805.08978v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bqbmg5qc4rb3zlf7gqilewh3sa">fatcat:bqbmg5qc4rb3zlf7gqilewh3sa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191023031106/https://arxiv.org/pdf/1805.08978v1.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/0b/a3/0ba3871e950c7889596340b47ee053d567284ff2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1805.08978v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

An approximation algorithm for network design problems with downwards-monotone demand functions

Michael Laszlo, Sumitra Mukherjee
<span title="2007-04-28">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5dkx5l3pkjclfd46nyh4eftsrq" style="color: black;">Optimization Letters</a> </i> &nbsp;
Building on an existing 2-approximate algorithm for the class of network design problems with downwards-monotone demand functions, many of which are NP-hard, we present an algorithm that produces solutions  ...  that are at least as good as and typically better than solutions produced by the existing algorithm.  ...  Proof Both algorithms may assign non-zero values only to edges in a minimum spanning tree M of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11590-007-0051-8">doi:10.1007/s11590-007-0051-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bgmm2aqicbczxf4kdin7bok64e">fatcat:bgmm2aqicbczxf4kdin7bok64e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090509042327/http://scis.nova.edu:80/~sumitra/paper/Laszlo_Mukherjee_Optimization_Letters_2008.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/d1/c2/d1c21bbfba4f81081ee05a9e875e78583be15912.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11590-007-0051-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Transit data-based MST computation

Thodoris Karatasos, Evi Papaioannou
<span title="2017-10-30">2017</span> <i title="The Institute for Research and Community Services (LPPM) ITB"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lpemckh6jfhehiaagnsspj5vmu" style="color: black;">Electronic Journal of Graph Theory and Applications</a> </i> &nbsp;
Our objective is to automatically transform real-world images to graphs and, then, compute Minimum Spanning Trees (MST) in them.  ...  In the next 50 years, several significantly faster algorithms were suggested, ranging from the algorithm by Fredman and Tarjan [8] , over algorithms with inverse-Ackermann-type complexity by Chazelle  ...  Kruskal's algorithm starts with an edge in the graph with minimum weight and builds the spanning tree by successively adding edges one by one into a growing spanning tree.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5614/ejgta.2017.5.2.6">doi:10.5614/ejgta.2017.5.2.6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vidxqbhqqjgkxj37dvf3xf7lgy">fatcat:vidxqbhqqjgkxj37dvf3xf7lgy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721135643/http://www.ejgta.org/index.php/ejgta/article/download/377/pdf_51" 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/78/2b/782b6c3fb4ba799d82eb424d0b86ed0027670670.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5614/ejgta.2017.5.2.6"> <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>

Geometric Lower Bounds for Parametric Matroid Optimization

D. Eppstein
<span title="">1998</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cu3ouk4pmzhsroy4l5k2c35xtu" style="color: black;">Discrete &amp; Computational Geometry</a> </i> &nbsp;
minimum spanning trees.  ...  We relate the sequence of minimum bases of a matroid with linearly varying weights to three problems from combinatorial geometry: k-sets, lower envelopes of line segments, and convex polygons in line arrangements  ...  The maximum complexity of a lower envelope of line segments is (nα(n)), where α is the inverse Ackermann function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/pl00009396">doi:10.1007/pl00009396</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ftgo2clnl5a2fcd6r6ol5xmjeu">fatcat:ftgo2clnl5a2fcd6r6ol5xmjeu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502092519/https://link.springer.com/content/pdf/10.1007%2FPL00009396.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/a0/a8/a0a87b55f9083825be0674f7283fe2dfa53e125c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/pl00009396"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Geometric lower bounds for parametric matroid optimization

David Eppstein
<span title="">1995</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC &#39;95</a> </i> &nbsp;
minimum spanning trees.  ...  We relate the sequence of minimum bases of a matroid with linearly varying weights to three problems from combinatorial geometry: k-sets, lower envelopes of line segments, and convex polygons in line arrangements  ...  The maximum complexity of a lower envelope of line segments is (nα(n)), where α is the inverse Ackermann function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/225058.225284">doi:10.1145/225058.225284</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/Eppstein95.html">dblp:conf/stoc/Eppstein95</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vmdbwosnh5alfgf2el4idhgryq">fatcat:vmdbwosnh5alfgf2el4idhgryq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20040407053525/http://www.ics.uci.edu:80/~eppstein/pubs/Epp-DCG-98.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/04/d8/04d868e8a2239df400e6fb19e93d8c63397d3a92.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/225058.225284"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Efficient determination of the k most vital edges for the minimum spanning tree problem

Cristina Bazgan, Sonia Toubaline, Daniel Vanderpooten
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zfqmu5yfvjbg3f4h6f7a5j3jr4" style="color: black;">Computers &amp; Operations Research</a> </i> &nbsp;
We study in this paper the problem of finding in a graph a subset of k edges whose deletion causes the largest increase in the weight of a minimum spanning tree.  ...  Efficient determination of the k most vital edges for the minimum spanning tree problem. Abstract.  ...  For the minimum spanning tree problem defined on a graph G with n vertices and m edges, Frederickson et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cor.2012.02.023">doi:10.1016/j.cor.2012.02.023</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/blexyofnn5djjmeaazcb4nflsq">fatcat:blexyofnn5djjmeaazcb4nflsq</a> </span>
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Efficient Algorithms for Finding the k Most Vital Edges for the Minimum Spanning Tree Problem [chapter]

Cristina Bazgan, Sonia Toubaline, Daniel Vanderpooten
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We study in this paper the problem of finding in a graph a subset of k edges whose deletion causes the largest increase in the weight of a minimum spanning tree.  ...  We propose for this problem an explicit enumeration algorithm whose complexity, when compared to the current best algorithm, is better for general k but very slightly worse for fixed k.  ...  For the minimum spanning tree problem defined on a graph G with n vertices and m edges, Frederickson et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-22616-8_11">doi:10.1007/978-3-642-22616-8_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yhkhls74djh5fkor35uq4fg6bm">fatcat:yhkhls74djh5fkor35uq4fg6bm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706031831/http://l1.lamsade.dauphine.fr/~bazgan/Papers/cocoa11.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/27/31/273121c3678e458584c999de184d17d71506fc6e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-22616-8_11"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Shortest Path Algorithm for Real-Weighted Undirected Graphs

Seth Pettie, Vijaya Ramachandran
<span title="">2005</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
inverse-Ackermann function, m the number of edges, and n the number of vertices.  ...  In an efficient preprocessing phase our algorithm creates a linear-size structure that facilitates single-source shortest path computations in O(m log α) time, where α = α(m, n) is the very slowly growing  ...  Theorem 6.1 shows that our SSSP algorithm is optimal among hierarchy-type algorithms, to within a tiny inverse-Ackermann factor.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539702419650">doi:10.1137/s0097539702419650</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/azfw3dgp7zdvzkqz6nh27x6ewy">fatcat:azfw3dgp7zdvzkqz6nh27x6ewy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100731095619/http://www.eecs.umich.edu/~pettie/papers/undsp.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/35/2a/352ab4215cebfd52ebfa4af4704104c427f40dc3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539702419650"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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