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### Computing the jump number on semi-orders is polynomial

A. von Arnim, C. de la Higuera
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
We first prove that semi-orders can be partitioned by serialization (or series decomposition) without loss of the jump number aspect.  ...  We then give a "divide-and-conquer" argument proving that to solve this case all we need is to be able to compute the number of maximal chains of length at least 2.  ...  The k-chum jump (bump) number Sk(P) (b,(P)) is the minimal number of jumps (maximal number bumps) for which a k-chain extension exists.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(94)90111-2">doi:10.1016/0166-218x(94)90111-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4f64dgvyjdhbebbn2nrhokaei">fatcat:b4f64dgvyjdhbebbn2nrhokaei</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190414111450/https://core.ac.uk/download/pdf/82350883.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/cd/f9/cdf966cc7ce6aa0cb8759d99f73b3ca97be402f8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(94)90111-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

### Page 8213 of Mathematical Reviews Vol. , Issue 99m [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;
We then study the jump maximization problem for proper interval graphs and series-parallel graphs.” W. G.  ...  From the summary: “We want to find a topolog- ical sequence that minimizes or maximizes the total number of jumps. ...  ...
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### Page 8175 of Mathematical Reviews Vol. , Issue 2004j [page]

<span title="">2004</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;
Variants of the result for bounded degree graphs, and for 3-connected graphs are also given. Hans L.  ...  The paper discusses recent advances and challenges in modelling and optimization for massive graphs such as the Call, Internet, Web and Market graphs.  ...
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### Interval dimension is a comparability invariant

Michel Habib, David Kelly, Rolf H. Möhring
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We show that orders with the same comparability graph have the same interval dimension, answering a question raised by Dagan, Golumbic and Pinter for finite orders.  ...  The interval dimension of an order is the minimum number of interval orders (on the same set) whose intersection is the given order.  ...  The analogous formula of Habib [9] for the jump number involves a similar substitution of graphs with two vertices for certain nodes.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(91)90010-y">doi:10.1016/0012-365x(91)90010-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nzyy6v7awjdjfptpoefzvzhski">fatcat:nzyy6v7awjdjfptpoefzvzhski</a> </span>
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### An algorithmic analysis of the Honey-Bee game

Rudolf Fleischer, Gerhard J. Woeginger
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In the solitaire version, the goal of the single player is to conquer the entire graph with the minimum number of moves.  ...  The solitaire version is NP-hard on trees and split graphs, but can be solved in polynomial time on co-comparability graphs.  ...  We will show that this is easy for co-comparability graphs (arbitrary number of colors), while it is NP-hard for split graphs (arbitrary number of colors), trees (four colors), and series-parallel graphs  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2012.05.032">doi:10.1016/j.tcs.2012.05.032</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k2yxncyzovhftcm45nm7wehlme">fatcat:k2yxncyzovhftcm45nm7wehlme</a> </span>
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### Transitive compaction in parallel via branchings

Phillip Gibbons, Richard Karp, Vijaya Ramachandran, Danny Soroker, Robert Tarjan
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anp7kqfyerdljfxydqb4objj6a" style="color: black;">Journal of Algorithms</a> </i> &nbsp;
Our main result is a parallel algorithm for this problem, which runs in polylog parallel time and uses O(n 3 ) processors on a PRAM.  ...  We also present sequential algorithms for the problem that run in time O(m + n ⋅ log n).  ...  The problem studied here is reminiscent of the well-studied problem of finding a maximal independent set of vertices in a graph, for which several parallel algorithms have appeared in the literature (  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0196-6774(91)90026-u">doi:10.1016/0196-6774(91)90026-u</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nshgtw7f5fc37jksb2hsl4lnna">fatcat:nshgtw7f5fc37jksb2hsl4lnna</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20050209215806/http://www.cs.utexas.edu:80/~vlr/papers/transcomp.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/b9/c1/b9c1b91d348b3f8558ca26491af611fe66074732.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0196-6774(91)90026-u"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

### Efficient parallel algorithms for chordal graphs

P.N. Klein
<span title="">1988</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v4uclqixrrhlnk5pbw4wii6cfq" style="color: black;">[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science</a> </i> &nbsp;
Savage and Wloka [41 have given an efficient parallel algorithm for optimum coloring of interval graphs.  ...  , finding a breadth-first search tree and a depth-first search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism.  ...  Thanks also to others with whom I discussed this research, including Dina Kravets, Tom Leighton, Charles Leiserson, George Lueker, Mark Novick, James Park, John Reif, Cliff Stein, and Joel Wein.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sfcs.1988.21933">doi:10.1109/sfcs.1988.21933</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/focs/Klein88.html">dblp:conf/focs/Klein88</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cdmk6ju75rbdfbxfcymexdrgwy">fatcat:cdmk6ju75rbdfbxfcymexdrgwy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060911160443/http://www.cs.brown.edu/research/pubs/pdfs/1996/Klein-1996-EPA.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/34/b4/34b46a16f746b6346fefd956ab211a71595befc5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sfcs.1988.21933"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### Project scheduling with irregular costs: complexity, approximability, and algorithms

Alexander Grigoriev, Gerhard J. Woeginger
<span title="">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnqseeosvrf6tnj6sc3lbn2y4e" style="color: black;">Acta Informatica</a> </i> &nbsp;
For precedence constraints with bounded height, there is a complexity jump from height one to height two: For height one, the problem is polynomially solvable, whereas for height two, it is NP-hard and  ...  Finally, the problem is shown to be polynomially solvable if the precedence constraints have bounded width or are series parallel.  ...  We thank Yuri Kochetov, Alexander Kononov, and Maxim Sviridenko for several helpful discussions and comments on the topic of this paper.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00236-004-0150-2">doi:10.1007/s00236-004-0150-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2khitidfuzdkjkdwh3cuf7llpq">fatcat:2khitidfuzdkjkdwh3cuf7llpq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705135547/http://digitalarchive.maastrichtuniversity.nl/fedora/get/guid%3A9812f5ab-67c1-4030-8933-55d68e30e821/ASSET1/" 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/f6/68/f668c117c3ea68fcd729032021268e565e62cc07.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00236-004-0150-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Project Scheduling with Irregular Costs: Complexity, Approximability, and Algorithms [chapter]

Alexander Grigoriev, Gerhard J. Woeginger
<span title="">2002</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;
For precedence constraints with bounded height, there is a complexity jump from height one to height two: For height one, the problem is polynomially solvable, whereas for height two, it is NP-hard and  ...  Finally, the problem is shown to be polynomially solvable if the precedence constraints have bounded width or are series parallel.  ...  We thank Yuri Kochetov, Alexander Kononov, and Maxim Sviridenko for several helpful discussions and comments on the topic of this paper.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36136-7_34">doi:10.1007/3-540-36136-7_34</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r3quua5hvndvvcckjzb5wgrhse">fatcat:r3quua5hvndvvcckjzb5wgrhse</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427213045/https://cris.maastrichtuniversity.nl/portal/files/1191181/guid-9812f5ab-67c1-4030-8933-55d68e30e821-ASSET1.0.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/0a/80/0a80327e317678b8150f557bb3c37271f6da1461.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36136-7_34"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### A fast exact simulation method for a class of Markov jump processes [article]

Yao Li, Lili Hu
<span title="2015-10-22">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our performance tests and CPU operation statistics show certain advantage of the HLM for large scale problems.  ...  A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper.  ...  Acknowledgement The authors would like to thank Lai-Sang Young, Kevin Lin, Markos Katsoulakis, and the anonymous reviewer for many enlightening discussions and constructive suggestions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.04802v2">arXiv:1506.04802v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f3zvfv3z7ffkrlmeoa6ezetjsm">fatcat:f3zvfv3z7ffkrlmeoa6ezetjsm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200913174855/https://arxiv.org/pdf/1506.04802v2.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/5d/0f/5d0f0a2cd2d4fa9ea9a88b67550baa064332ed47.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.04802v2" 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>

### Scheduling under Uncertainty: Bounding the Makespan Distribution [chapter]

Rolf H. Möhring
<span title="">2001</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;
Deterministic models for project scheduling and control suffer from the fact that they assume complete information and neglect random influences that occur during project execution.  ...  This article presents a survey on the reasons for this phenomenon, its complexity, and on methods how to obtain more relevant information.  ...  A proper choice is to consider series-parallel networks, since then the computation reduces to a sequence of convolutions and products of distribution functions.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45506-x_7">doi:10.1007/3-540-45506-x_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/loaenftpnvcnnd5zob3tays7ti">fatcat:loaenftpnvcnnd5zob3tays7ti</a> </span>
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### Design of Decision-Making Organizations

Michael Christensen, Thorbjørn Knudsen
<span title="">2010</span> <i title="Institute for Operations Research and the Management Sciences (INFORMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zncv5noo7jgodckylffhkp26cq" style="color: black;">Management science</a> </i> &nbsp;
We provide general proofs that show how decision-making structures can be constructed so they maximize reliability for a given number of agents.  ...  It is thereby useful for assessment of the many complicated hybrid structures that we see in actual decision-making organizations, such as banks, purchasing departments, and military intelligence.  ...  March, Roy Radner, Raaj Sah, Larry Samuelson, and Nils Stieglitz for discussions and helpful comments on previous drafts.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1287/mnsc.1090.1096">doi:10.1287/mnsc.1090.1096</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tstughmdzvgp7hwlkysj3v5zdm">fatcat:tstughmdzvgp7hwlkysj3v5zdm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303085408/http://pdfs.semanticscholar.org/c621/aba6662d957b04b88fbdb427e7481d7fa00e.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/c6/21/c621aba6662d957b04b88fbdb427e7481d7fa00e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1287/mnsc.1090.1096"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

### A Finite Time Combinatorial Algorithm for Instantaneous Dynamic Equilibrium Flows [article]

Lukas Graf, Tobias Harks
<span title="2022-04-24">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, all existence results and computational methods are based on fixed-point theorems and numerical discretization schemes and no exact finite time algorithm for equilibrium computation is known  ...  Although IDE have been studied for decades, several fundamental questions regarding equilibrium computation and complexity are not well understood.  ...  Acknowledgments: We are grateful to the anonymous reviewers for their valuable feedback on this paper. Additionally, we thank the Deutsche Forschungsgemeinschaft (DFG) for their financial support.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.07808v4">arXiv:2007.07808v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bybdx36rvncztcua53qg7yjhiu">fatcat:bybdx36rvncztcua53qg7yjhiu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220506191129/https://arxiv.org/pdf/2007.07808v4.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/df/2f/df2f75f1423792b6183d432ee452ea8d0bd1dc3a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.07808v4" 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>

### Reference list of indexed articles

<span title="">2000</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Steiner, A compact labeling scheme for series-parallel graphs 11 (1985) 281-297 313. 1J.J. Aalbersberg and G.  ...  Habib, Jump number of dags having Dilworth number 2 7 ( 1984) 243-250 211. M. Conforti and G.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-218x(00)00209-2">doi:10.1016/s0166-218x(00)00209-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l53yxlj45ffdrdecl3uah2gj3y">fatcat:l53yxlj45ffdrdecl3uah2gj3y</a> </span>
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### Logarithmic Time Parallel Bayesian Inference [article]

David M. Pennock
<span title="2013-01-30">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel random-access machine) with n processors, for any constant number  ...  I present a parallel algorithm for exact probabilistic inference in Bayesian networks.  ...  Acknowledgments Thanks to David Pynadath and to the anonymous reviewers.  ...
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