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Solving #SAT using vertex covers

Naomi Nishimura, Prabhakar Ragde, Stefan Szeider
<span title="2007-09-03">2007</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 the backdoor set detection we utilize an efficient vertex cover algorithm applied to a certain "obstruction graph" that we associate with the given formula.  ...  We conclude that for every deletion pair {X, Y } of F either X ⊆ B or Y ⊆ B must be the case. ⊓ ⊔ Finding Backdoor Sets Using Vertex Covers For a formula F let G F denote the graph with vertex set var  ...  In this paper we extend the algorithmic use of backdoor sets for SAT to the counting problem #SAT.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00236-007-0056-x">doi:10.1007/s00236-007-0056-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/onhqc2ooj5fxjduv4ubachwn6e">fatcat:onhqc2ooj5fxjduv4ubachwn6e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829031114/https://cs.uwaterloo.ca/~plragde/papers/sharpsat_AI.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/a8/44/a844a70b8bbdf6502a481c6c035af94d29afe7c1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00236-007-0056-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Solving #SAT Using Vertex Covers [chapter]

Naomi Nishimura, Prabhakar Ragde, Stefan Szeider
<span title="">2006</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 the backdoor set detection we utilize an efficient vertex cover algorithm applied to a certain "obstruction graph" that we associate with the given formula.  ...  We conclude that for every deletion pair {X, Y } of F either X ⊆ B or Y ⊆ B must be the case. ⊓ ⊔ Finding Backdoor Sets Using Vertex Covers For a formula F let G F denote the graph with vertex set var  ...  In this paper we extend the algorithmic use of backdoor sets for SAT to the counting problem #SAT.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11814948_36">doi:10.1007/11814948_36</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yid72omhwnckjmr7yxi46t3ppm">fatcat:yid72omhwnckjmr7yxi46t3ppm</a> </span>
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A New Solver for the Minimum Weighted Vertex Cover Problem [chapter]

Hong Xu, T. K. Satish Kumar, Sven Koenig
<span title="">2016</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Given a vertex-weighted graph G = V, E , the minimum weighted vertex cover (MWVC) problem is to choose a subset of vertices with minimum total weight such that every edge in the graph has at least one  ...  In this paper, we present a new solver for the MWVC problem based on a novel reformulation to a series of SAT instances using a primal-dual approximation algorithm as a starting point.  ...  A minimum vertex cover (MVC) of G is a vertex cover of minimum cardinality.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-33954-2_28">doi:10.1007/978-3-319-33954-2_28</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jyqb3a37nvgk5oxqe63rqqwgei">fatcat:jyqb3a37nvgk5oxqe63rqqwgei</a> </span>
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Solving minones-2-sat as Fast as vertex cover [chapter]

Neeldhara Misra, N. S. Narayanaswamy, Venkatesh Raman, Bal Sri Shankar
<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;
It generalizes the well-studied problem of finding the smallest vertex cover of a graph, which can be modeled using a 2-SAT formula with no negative literals.  ...  In this paper, we present a polynomial-time reduction from min ones 2-sat to vertex cover without increasing the parameter and ensuring that the number of vertices in the reduced instance is equal to the  ...  While chitting set has a k O(c) kernel [AK07], a polynomial sized kernel is unlikely for min ones c-sat even for c = 3, as a special case of min ones 3-sat (not-1-in-3 SAT) is unlikely to have a polynomial  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-15155-2_48">doi:10.1007/978-3-642-15155-2_48</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n2gni3uyynhpdm5bccghhrgtl4">fatcat:n2gni3uyynhpdm5bccghhrgtl4</a> </span>
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Satisfiability of mixed Horn formulas

Stefan Porschen, Ewald Speckenmeyer
<span title="">2007</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 further show that the NP-hard optimization problem minimum weight SAT for mixed Horn formulas can be solved in time O(2 0.5284n ) if non-negative weights are assigned to the variables.  ...  We show that SAT remains NP-complete for such instances and also that any CNF formula can be encoded in terms of a mixed Horn formula in polynomial time.  ...  It is the part P := P (M) that can be transformed into a Horn formula using a minimum vertex cover of G P as essential set.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2007.02.010">doi:10.1016/j.dam.2007.02.010</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7gxh6rf2yjhi7cewoh4pewpek4">fatcat:7gxh6rf2yjhi7cewoh4pewpek4</a> </span>
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On the existence of subexponential parameterized algorithms

Liming Cai, David Juedes
<span title="">2003</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;
Cover, and Independent Set on planar graph instances. r  ...  oðnÞ Þ: These results are also applied to show evidence for the non-existence of Oð2 oð ffiffi k p Þ pðnÞÞ-time parameterized algorithms for a number of other important problems such as Dominating Set, Vertex  ...  By using these results in combination with a reduction to kernal, we show in Theorem 4.3 that Vertex Cover-3 can be solved in Oð2 oðkÞ pðnÞÞ steps if and only if 3-SAT is in DTIMEð2 oðnÞ Þ; where n is  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(03)00074-6">doi:10.1016/s0022-0000(03)00074-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m7u6kffamfditepzv3ktkhwhry">fatcat:m7u6kffamfditepzv3ktkhwhry</a> </span>
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Cardinality Encodings for Graph Optimization Problems

Alexey Ignatiev, Antonio Morgado, Joao Marques-Silva
<span title="">2017</span> <i title="International Joint Conferences on Artificial Intelligence Organization"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vfwwmrihanevtjbbkti2kc3nke" style="color: black;">Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence</a> </i> &nbsp;
Existing propositional encodings render impractical the use of propositional satisfiability (SAT) and maximum satisfiability (MaxSAT) solvers for solving a variety of these problems on large graphs.  ...  More importantly, the experimental results show that the proposed encoding enables existing SAT solvers to compute a maximum clique for large sparse networks, often more efficiently than the state of the  ...  For each picked vertex v ∈ V , add clause (¬x u ∨ ¬x v ). Moreover, the iterative SAT solving approach can exploit standard techniques commonly used in SAT-based problem solving.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.24963/ijcai.2017/91">doi:10.24963/ijcai.2017/91</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ijcai/IgnatievMM17.html">dblp:conf/ijcai/IgnatievMM17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lqn5v4tw2ne6jmvonj54xs54ma">fatcat:lqn5v4tw2ne6jmvonj54xs54ma</a> </span>
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Accelerating combinatorial filter reduction through constraints [article]

Yulin Zhang, Hazhar Rahmani, Dylan A. Shell, Jason M. O'Kane
<span title="2020-11-06">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots.  ...  Hence, to solve FM, we can always look for vertex covers. B. Searching over vertex covers via variables Now we represent a vertex cover with binary variables.  ...  Otherwise, if the SAT [k] has not been solved within the time budget, then we use the minimum cover found so far to construct the minimal filter (line 16).  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.03471v1">arXiv:2011.03471v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mevttxoxq5dz5nmids2il6rtke">fatcat:mevttxoxq5dz5nmids2il6rtke</a> </span>
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Tight lower bounds for certain parameterized NP-hard problems

Jianer Chen, Benny Chor, Mike Fellows, Xiuzhen Huang, David Juedes, Iyad A. Kanj, Ge Xia
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted sat, hitting set, set cover, and feature set, cannot be solved in time n o(k) m O(1) , where n is  ...  Chen et al. / Information and Computation 201 (2005) 216-231 217 that another group of parameterized problems which includes weighted q-sat (for any fixed q 2), clique, independent set, and dominating  ...  The class SNP [18] contains many well-known NP-hard problems including q-sat, q-colorability, q-set cover, vertex cover, and independent set [15] .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2005.05.001">doi:10.1016/j.ic.2005.05.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hsr2rjvgezeozfunj3kdv77ij4">fatcat:hsr2rjvgezeozfunj3kdv77ij4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808124431/http://www.mrfellows.net/papers/C-61-CCC-7authors.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/87/a7/87a71dab2c7f27f89777391f6dbac4c271f8ba7b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2005.05.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Neighbourhood Evaluation Criteria for Vertex Cover Problem [article]

Kaustubh K Joshi
<span title="2020-05-07">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Neighbourhood Evaluation Criteria is a heuristical approximate algorithm that attempts to solve the Minimum Vertex Cover. degree count is kept in check for each vertex and the highest count based vertex  ...  is included in our cover set.  ...  This in term helps to solve various other NP problems (Circuit SAT, Max Clique selection [10] ,etc.) which can be reduced to a SAT problem.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.05065v1">arXiv:2005.05065v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7tbejfmrvzgvxgulussuwspaay">fatcat:7tbejfmrvzgvxgulussuwspaay</a> </span>
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The PACE 2019 Parameterized Algorithms and Computational Experiments Challenge: The Fourth Iteration (Invited Paper)

M. Ayaz Dzulfikar, Johannes K. Fichte, Markus Hecher, Michael Wagner
<span title="2019-12-11">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tpdnk2xs3fdn5moccz7npe5s24" style="color: black;">International Symposium on Parameterized and Exact Computation</a> </i> &nbsp;
from SAT to clique and then clique to vertex cover into one).  ...  , where we took widely used SAT instances, reduced them into 3-SAT instances [133] and then reduced them to k-vertex cover by means of the well-known reductions by Karp [104] (merge the reductions  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.ipec.2019.25">doi:10.4230/lipics.ipec.2019.25</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iwpec/DzulfikarFH19.html">dblp:conf/iwpec/DzulfikarFH19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i4goqilhxzbwrfhishxtwfhktu">fatcat:i4goqilhxzbwrfhishxtwfhktu</a> </span>
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Exact MinSAT Solving [chapter]

Chu Min Li, Felip Manyà, Zhe Quan, Zhu Zhu
<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;
We present an original approach to exact MinSAT solving based on solving MinSAT using MaxSAT encodings and MaxSAT solvers, and provide empirical evidence that our generic approach is competitive.  ...  As benchmarks, we used randomly generated Min-2-SAT and Min-3-SAT instances.  ...  0.00 0.02 0.01 0.00 2710 1995 ratios solved for Min-3-SAT were 4.25 and 5.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14186-7_33">doi:10.1007/978-3-642-14186-7_33</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d3n4sm6x2zecvfax467dvfrfie">fatcat:d3n4sm6x2zecvfax467dvfrfie</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190307055323/http://pdfs.semanticscholar.org/dbde/bb18b02f2a7ccf9711ea4f1837b53a21653d.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/db/de/dbdebb18b02f2a7ccf9711ea4f1837b53a21653d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14186-7_33"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

LP can be a cure for Parameterized Problems

N.S. Narayanaswamy, Venkatesh Raman, M.S. Ramanujan, Saket Saurabh, Marc Herbstritt
<span title="2012-02-24">2012</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/npfxqbtrtjcmndol3ijtu4shem" style="color: black;">Symposium on Theoretical Aspects of Computer Science</a> </i> &nbsp;
Then, using known and new reductions, we give O * (2.6181 k ) algorithms for the parameterized versions of Above Guarantee Vertex Cover, Odd Cycle Transversal, Split Vertex Deletion and Almost 2-SAT, and  ...  We also observe that using our algorithm, one can obtain a simple kernel for the classical vertex cover problem with at most 2k − O(log k) vertices.  ...  Recently, in [13] , a significantly faster algorithm for Vertex Cover above LP, running in time O * (2.3146 k ), has been obtained.  ...
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On Parameterized Exponential Time Complexity [chapter]

Jianer Chen, Iyad A. Kanj, Ge Xia
<span title="">2009</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 then illustrate how this equivalence can be used to show that special instances of parameterized NP-hard problems are as difficult as the general instances.  ...  We show that a parameterized problem can be solved in parameterized 2 o(f (k)) p(n) time if and only if it is solvable in time O(2 δf (k) q(n)) for any constant δ > 0, where p and q are polynomials.  ...  Cai and Juedes [5] proved that certain parameterized problems such as Vertex Cover, Max Cut, Max c-Sat cannot be solved in 2 o(k) p(n) time unless ETH fails, which is unlikely according to the common  ...
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On parameterized exponential time complexity

Jianer Chen, Iyad A. Kanj, Ge Xia
<span title="">2009</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;
We then illustrate how this equivalence can be used to show that special instances of parameterized NP-hard problems are as difficult as the general instances.  ...  We show that a parameterized problem can be solved in parameterized 2 o(f (k)) p(n) time if and only if it is solvable in time O(2 δf (k) q(n)) for any constant δ > 0, where p and q are polynomials.  ...  Cai and Juedes [5] proved that certain parameterized problems such as Vertex Cover, Max Cut, Max c-Sat cannot be solved in 2 o(k) p(n) time unless ETH fails, which is unlikely according to the common  ...
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