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Deciding Graph non-Hamiltonicity via a Closure Algorithm [article]

E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell, A. Lee
<span title="2016-11-05">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n!  ...  G is decided non-Hamiltonian. Over 100 non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian.  ...  For special classes of graphs, we believe that the WCA can be developed as a technique that always decides graph non-Hamiltonicity e.g. snarks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1611.01710v1">arXiv:1611.01710v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xu3eai2fuvcbxfxbx4xamf3vam">fatcat:xu3eai2fuvcbxfxbx4xamf3vam</a> </span>
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Deciding Graph non-Hamiltonicity via a Closure Algorithm

E Swart, Stephen Gismondi, N Swart, C Bell, A Lee
<span title="">2016</span> <i > S. J. Gismondi / Journal of Algorithms and Computation </i> &nbsp; <span class="release-stage">unpublished</span>
ARTICLE INFO We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n!  ...  Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n!  ...  We then present the O(n 8 ) Weak Closure Algorithm (WCA) that deduces values of 0/1 variables via Boolean closure (in place of LP) and non-matching.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gkmwnui2snae3fc454na7pr7cm">fatcat:gkmwnui2snae3fc454na7pr7cm</a> </span>
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Using Matching to Detect Infeasibility of Some Integer Programs [article]

S.J. Gismondi, E.R.Swart
<span title="2017-03-04">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We successfully apply the algorithm to a small set of specially formulated infeasible zero-one IP instances of the Hamilton cycle decision problem.  ...  The algorithm input is a set of nested doubly stochastic subsystems and a set E of instance defining variables set at zero level.  ...  For Ted, Pal was a colleague, co-author and friend. For myself (Gismondi), Pal taught me analysis, an understanding of convex polyhedra, and later became a colleague.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1703.01532v1">arXiv:1703.01532v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x4vhx5zu4jgyjh7w2j7jznr5ci">fatcat:x4vhx5zu4jgyjh7w2j7jznr5ci</a> </span>
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Backtracking (the) Algorithms on the Hamiltonian Cycle Problem [article]

Joeri Sleegers, Daan van den Berg
<span title="2021-07-01">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In a more general algorithmic assessment, we conjecture that edge pruning and non-Hamiltonicity checks might be largely responsible for these recursive savings.  ...  If the number of edges is either much higher or much lower, the problem is not hard – most backtracking algorithms decide such instances in (near) polynomial time.  ...  There are four such non-Hamiltonicity checks and it should be noted that indeed all of them are negative: they can only decide graphs to be either 'surely non-Hamiltonian' or 'undecided'.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2107.00314v1">arXiv:2107.00314v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fnvtens2jjfpbognu57dlg55qq">fatcat:fnvtens2jjfpbognu57dlg55qq</a> </span>
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Page 5992 of Mathematical Reviews Vol. , Issue 94j [page]

<span title="">1994</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;
A final re- sult of this paper is that all operators definable via a finite number of rules in a format due to de Simone are derived operators in the simple process calculus PC.”  ...  Oscar H. (1-UCSB-C; Santa Barbara, CA); Jiang, Tao [Jiang, Tao"] (3-MMAS-C; Hamilton, ON); Tran, Nicholas (1-UCSB-C; Santa Barbara, CA); Wang, Hui (1-ALH-C; Huntsville, AL) New decidability results concerning  ... 
<span class="external-identifiers"> </span>
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Page 3065 of Mathematical Reviews Vol. , Issue 96e [page]

<span title="">1996</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;
The novel idea of Jiirgen Dix consists in associating to any semantics SEM a sceptical non-monotonic entailment relation SEM‘, and investi- gating its non-monotonic properties.  ...  Ryszard Janicki (3-MMAS-C; Hamilton, ON) 96e:68079 68Q50 Parisi-Presicce, Francesco (I-ROME-IS; Rome); Piersanti, Gabriele (I-LAQL-PM; L’Aquila) Multilevel graph grammars.  ... 
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The Power of Local Computations in Graphs with Initial Knowledge [chapter]

Emmanuel Godard, Yves Métivier, Anca Muscholl
<span title="">2000</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 refine a proof technique based on coverings in order to cope with additional knowledge.  ...  Similarly, we show that election in ambiguous graphs is impossible, even if the graph topology is known by every node.  ...  This research was partly supported by the French-German project PROCOPE and by the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems) through the University of Bordeaux.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-46464-8_6">doi:10.1007/978-3-540-46464-8_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/codyatreine7faw6pemokwtpnm">fatcat:codyatreine7faw6pemokwtpnm</a> </span>
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Tight Polynomial Bounds for Loop Programs in Polynomial Space [article]

A. M. Ben-Amram, G. W. Hamilton
<span title="2021-11-10">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The main contribution is a new, space-efficient analysis algorithm. This algorithm is obtained in a few steps.  ...  First, we develop an algorithm for univariate bounds, a sub-problem which is already PSPACE-hard.  ...  The Closure Algorithm In this section, we present a version of the algorithm of [BAH20] , computing in exponential space and time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.02823v4">arXiv:2010.02823v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yzbekrynpvaalbvhz5htbylxia">fatcat:yzbekrynpvaalbvhz5htbylxia</a> </span>
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Fast Exact Algorithms for Hamiltonicity in Claw-Free Graphs [chapter]

Hajo Broersma, Fedor V. Fomin, Pim van 't Hof, Daniël Paulusma
<span title="">2010</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 a claw-free graph G, finding a hamiltonian cycle is equivalent to finding a closed trail (eulerian subgraph) that dominates the edges of some associated graph H.  ...  The latter algorithm also finds a hamiltonian cycle if it exists.  ...  For any integer k ≥ 1, a graph H is called k-degenerate if every non-empty subgraph of H has a vertex of degree at most k.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-11409-0_4">doi:10.1007/978-3-642-11409-0_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/shzn3ahrn5bu3gpsszw4cpsnji">fatcat:shzn3ahrn5bu3gpsszw4cpsnji</a> </span>
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Faster Deciding MSO Properties of Trees of Fixed Height, and Some Consequences

Jakub Gajarsky, Petr Hlineny, Marc Herbstritt
<span title="2012-12-10">2012</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yjwtenvm3vc4tjdmag7doffpby" style="color: black;">Foundations of Software Technology and Theoretical Computer Science</a> </i> &nbsp;
This yields a faster MSO model checking algorithm for trees of bounded height than the one for general trees.  ...  This makes bounded shrub-depth a good candidate for characterization of the hereditary classes of graphs on which FO and MSO 1 coincide, a problem recently posed by Elberfeld, Grohe, and Tantau (LICS 2012  ...  In a more general perspective, our algorithm can be straightforwardly applied to any suitable "depth-structured" graph class via efficient interpretability of logic theories.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.fsttcs.2012.112">doi:10.4230/lipics.fsttcs.2012.112</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fsttcs/GajarskyH12.html">dblp:conf/fsttcs/GajarskyH12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wit3in442fe4pn23tikkr6d54y">fatcat:wit3in442fe4pn23tikkr6d54y</a> </span>
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Tree-width and Logspace: Determinants and Counting Euler Tours [article]

Nikhil Balaji, Samir Datta
<span title="2013-12-31">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
of a bounded tree-width graph and prove that it is L-complete.  ...  Finally, we also show some linear algebraic extensions of the determinant algorithm to show how to compute the charcteristic polynomial and trace of the powers of a bounded tree-width graph in L.  ...  For example, Hamiltonicity is an MSO property and hence deciding if a bounded treewidth graph has a Hamiltonian cycle can be done in linear time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1312.7468v2">arXiv:1312.7468v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cfyu5jvox5hnzjyinydlsxethi">fatcat:cfyu5jvox5hnzjyinydlsxethi</a> </span>
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On the complexity of the parity argument and other inefficient proofs of existence

Christos H. Papadimitriou
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
, and the Borsuk-Ulam theorem, the linear complementarity problem for P-matrices, finding a mixed equilibrium in a non-zero sum game, finding a second Hamilton circuit in a Hamiltonian cubic graph, a second  ...  The existence of the solution sought is established via a simple graph-theoretic argument with an inefficiently constructive proof; for example, PLS can be thought of as corresponding to the lemma "every  ...  ), there is a non-empty induced graph with an even number of edges from each class.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(05)80063-7">doi:10.1016/s0022-0000(05)80063-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dhwxgublf5cjbmupdgi4x24uwa">fatcat:dhwxgublf5cjbmupdgi4x24uwa</a> </span>
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Exact Algorithms for Finding Longest Cycles in Claw-Free Graphs

Hajo Broersma, Fedor V. Fomin, Pim van 't Hof, Daniël Paulusma
<span title="2011-09-26">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
The Hamiltonian Cycle problem is the problem of deciding whether an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem.  ...  Using this translation we obtain two deterministic algorithms that solve the Longest Cycle problem, and consequently the Hamiltonian Cycle problem, for claw-free graphs: one algorithm that uses O * (1.6818  ...  graph H of the closure of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-011-9576-4">doi:10.1007/s00453-011-9576-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4amjcwpgzjh3dlcntei2lxslc4">fatcat:4amjcwpgzjh3dlcntei2lxslc4</a> </span>
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Model Checking Lower Bounds for Simple Graphs

Michael Lampis, Martin Grohe
<span title="2014-03-25">2014</span> <i title="Logical Methods in Computer Science e.V."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c67srop7pbe3nciquoxzy3d6pm" style="color: black;">Logical Methods in Computer Science</a> </i> &nbsp;
A well-known result by Frick and Grohe shows that deciding FO logic on trees involves a parameter dependence that is a tower of exponentials.  ...  Though this lower bound is tight for Courcelle's theorem, it has been evaded by a series of recent meta-theorems for other graph classes.  ...  A previous version of this paper used the assumption that EXP = NEXP.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-10(1:18)2014">doi:10.2168/lmcs-10(1:18)2014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l3it53de4zcjvk46d57haouxem">fatcat:l3it53de4zcjvk46d57haouxem</a> </span>
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Model Checking Lower Bounds for Simple Graphs [chapter]

Michael Lampis
<span title="">2013</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;
A well-known result by Frick and Grohe shows that deciding FO logic on trees involves a parameter dependence that is a tower of exponentials.  ...  Though this lower bound is tight for Courcelle's theorem, it has been evaded by a series of recent meta-theorems for other graph classes.  ...  A previous version of this paper used the assumption that EXP = NEXP.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-39206-1_57">doi:10.1007/978-3-642-39206-1_57</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mrxkaraatvhzrjjtk4bhfpv4ii">fatcat:mrxkaraatvhzrjjtk4bhfpv4ii</a> </span>
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