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Approximating Max-Cut under Graph-MSO Constraints [article]

Martin Koutecký, Jon Lee, Viswanath Nagarajan, Xiangkun Shen
2018 arXiv   pre-print
We consider the max-cut and max-k-cut problems under graph-based constraints. Our approach can handle any constraint specified using monadic second-order (MSO) logic on graphs of constant treewidth.  ...  We give a 1/2-approximation algorithm for this class of problems.  ...  Therefore, we immediately obtain 1 2 -approximation algorithms for max-cut under any MSO graph constraint.  ... 
arXiv:1803.05718v2 fatcat:kyhf3ahwvjbhhk7nrn7yv2fjxa

Graph-transformation verification using monadic second-order logic

Kazuhiro Inaba, Soichiro Hidaka, Zhenjiang Hu, Hiroyuki Kato, Keisuke Nakano
2011 Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming - PPDP '11  
The logic-based foundation allows to express the schema satisfaction of transformations as the validity of MSO formulas over graph structures.  ...  We tackle the problem by first reformulating the semantics of UnCAL into monadic second-order logic (MSO).  ...  The inverse image of an MSO-definable set of graphs under an MSO-definable transduction system is MSO-definable.  ... 
doi:10.1145/2003476.2003482 dblp:conf/ppdp/InabaHHKN11 fatcat:p5sehv2ycnfazp24dxxz4w3sxm

Multi-Searcher Optimization for the Optimal Energy Dispatch of Combined Heat and Power-Thermal-Wind-Photovoltaic Systems

Jianlin Tang, Tao Yu, Xiaoshun Zhang, Zhuohuan Li, Junbin Chen
2019 Applied Sciences  
The available power of wind turbine (WT) units and photovoltaic (PV) units is approximated with the probability density functions of wind speed and solar irradiance, respectively.  ...  This paper proposes a novel multi-searcher optimization (MSO) algorithm for the optimal energy dispatch (OED) of combined heat and power-thermal-wind-photovoltaic systems.  ...  and cut-out wind speeds, respectively.  ... 
doi:10.3390/app9030537 fatcat:istfvqbw4rfbdc6m2suom7rbqy

Practical algorithms for MSO model-checking on tree-decomposable graphs

Alexander Langer, Felix Reidl, Peter Rossmanith, Somnath Sikdar
2014 Computer Science Review  
A celebrated theorem in this area by Courcelle states that any graph problem expressible in MSO can be solved in linear time on graphs that admit a tree-decomposition of constant width.  ...  Monadic second-order (MSO) logic allows quantifications over unary relations (sets) and can be used to express a host of useful graph properties such as connectivity, c-colorability (for a fixed c), Hamiltonicity  ...  problems with connectivity constraints.  ... 
doi:10.1016/j.cosrev.2014.08.001 fatcat:4eogxn65frdy5hr7syli5qjd5m

Extension Complexity, MSO Logic, and Treewidth [article]

Petr Kolman, Martin Koutecký, Hans Raj Tiwary
2020 arXiv   pre-print
We consider the convex hull P_φ(G) of all satisfying assignments of a given MSO formula φ on a given graph G.  ...  This implies that our extension of P_φ(G) is decomposable and has a constraint matrix of bounded treewidth; so far only few classes of polytopes are known to be decomposable.  ...  Acknowledgements We thank the anonymous reviewers for pointing out existing work, a shorter proof of the Glueing lemma, and clarifying the distinctions between MSO 1 and MSO 2 , among various other improvements  ... 
arXiv:1507.04907v9 fatcat:3z3rpkfwbvffhji6vtdbqkfhpm

Extension Complexity, MSO Logic, and Treewidth

Petr Kolman, Martin Koutecký, Hans Raj Tiwary
2019 Discrete Mathematics & Theoretical Computer Science  
We consider the convex hull $P_{\varphi}(G)$ of all satisfying assignments of a given MSO formula $\varphi$ on a given graph $G$.  ...  As a corollary of our main result, we obtain an analogous result % for the weaker MSO$_1$ logic on the wider class of graphs of bounded cliquewidth.  ...  Acknowledgements We thank the anonymous reviewers for pointing out existing work, a shorter proof of the Glueing lemma, and clarifying the distinctions between MSO 1 and MSO 2 , among various other improvements  ... 
doi:10.23638/dmtcs-22-4-8 fatcat:bt354gly3veejgspc4qamj6ixq

A logic-based algorithmic meta-theorem for mim-width [article]

Benjamin Bergougnoux, Jan Dreier, Lars Jaffke
2022 arXiv   pre-print
This results in algorithms with tight run times under the Exponential Time Hypothesis (𝖤𝖳𝖧) for tree-width and clique-width; the above mentioned run time for mim-width is nearly tight under the 𝖤𝖳𝖧  ...  We introduce a logic called distance neighborhood logic with acyclicity and connectivity constraints (𝖠&𝖢 𝖣𝖭 for short) which extends existential 𝖬𝖲𝖮_1 with predicates for querying neighborhoods  ...  A simple Turing-reduction from the NPhard [44] Max Cut problem shows that Exact Cut is also NP-hard (by trying out all values for k).  ... 
arXiv:2202.13335v1 fatcat:nft3dmarxnczdbkhuo4n4wnmoy

Width Parameters Beyond Tree-width and their Applications

P. Hlineny, S.-i. Oum, D. Seese, G. Gottlob
2007 Computer journal  
Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth.  ...  In this contribution, we demonstrate how 'width' parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the  ...  In the definition of rank-width, we replace the cut-rank functions by max (i G (X), i G (Y)) to obtain the definition of symmetric cliquewidth.  ... 
doi:10.1093/comjnl/bxm052 fatcat:n4nbasuvubc5lkajkskqk22fey

On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic [article]

Stephan Kreutzer, Siamak Tazari
2009 arXiv   pre-print
Using our results from the first part of our work we establish a strong lower bound for tractability of MSO on classes of colored graphs.  ...  The second part of our work deals with providing a lower bound to Courcelle's famous theorem, stating that every graph property that can be expressed by a sentence in monadic second-order logic (MSO),  ...  In order to find such a set, we use the ideas in the approximation algorithm for treewidth, where sparse cuts are used to construct balanced cuts and balanced cuts are, in turn, used to construct a tree  ... 
arXiv:0907.3076v1 fatcat:ajfgzk6oqregpiwfrvvkec3viu

A Generalization of the Łoś-Tarski Preservation Theorem - Dissertation Summary [article]

Abhisekh Sankaran
2018 arXiv   pre-print
The constructive aspects of the proofs of the model-theoretic results of the dissertation are used to obtain (algorithmic) meta-kernels for various dense graphs such as graphs of bounded clique-width and  ...  subclasses of these like m-partite cographs and graph classes of bounded shrub-depth.  ...  Max-SAT/Max-r-SAT P SC(k) 20. Vertex Multiway Cut P SC(k) 21. Multicolored Biclique P SC(2k) 22.  ... 
arXiv:1811.01014v1 fatcat:vurmh3kcrbgtve7yp6lqngflpy

Analyzing Timed Systems Using Tree Automata [article]

S. Akshay, Paul Gastin, Shankara Narayanan Krishna
2017 arXiv   pre-print
The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints.  ...  When a family of graphs has bounded tree-width, they can be interpreted in trees and MSO-definable properties of such graphs can be checked using tree automata.  ...  At the very least, we would obtain new width-based under-approximations which may lead to new decidability results. Figure 1 : 1 A timed automaton (top) with 2 clocks x, y.  ... 
arXiv:1604.08443v3 fatcat:hsgq6ornprah3hl6h34jac65aa

Diagnosis for Control and Decision Support for Autonomous Vehicles [chapter]

Mogens Blanke, Søren Hansen, Morten Rufus Blas
2016 Complex Systems  
An MSO set is a subgraph where only one constraint can be removed to get a justdetermined part of the graph.  ...  An MSO set contains a complete matching plus one unmatched constraint, and one redundancy relation is available from each MSO set.  ... 
doi:10.1007/978-3-319-28860-4_1 fatcat:ud2thn5bpfdlziauier6rd7g4a

Space complexity: what makes planar graphs special?

Samir Datta, Raghav Kulkarni
2013 Bulletin of the European Association for Theoretical Computer Science  
There are several new efficient algorithms for a variety of graph optimization problems that exploit planarity and, in general, the structure of low genus graphs and graphs with excluded minors.  ...  They discuss several properties of planar graphs and their precise role in the design of space efficient algorithms.  ...  Space Complexity of Max-Cut in Planar Graphs We have observed that Max-Cut in planar graphs admits UL ∩ co − UL approximation scheme.  ... 
dblp:journals/eatcs/DattaK13 fatcat:errya5hbabeg5bh2qph5yobtiy

Linear kernels for edge deletion problems to immersion-closed graph classes [article]

Archontia C. Giannopoulou, Michał Pilipczuk, Dimitrios M. Thilikos, Jean-Florent Raymond, Marcin Wrochna
2016 arXiv   pre-print
We prove that whenever all graphs from F are connected and at least one graph of F is planar and subcubic, then the F-Immersion Deletion problem admits: a constant-factor approximation algorithm running  ...  [FOCS 2012], who obtained a similar set of algorithmic results for F-Minor Deletion, under the assumption that at least one graph from F is planar.  ...  Furthermore, p is closed under disjoint union if p(G 1 G 2 ) = max(p(G 1 ), p(G 2 )), for any two graphs G 1 and G 2 ; here, denotes the disjoint union of two graphs.  ... 
arXiv:1609.07780v1 fatcat:uzgswbuyhvacrirs5e75kcapnu

Towards an Efficient Tree Automata based technique for Timed Systems [article]

S. Akshay, Paul Gastin, Shankara Narayanan Krishna, Ilias Sarkar
2017 arXiv   pre-print
Our technique consists of modeling the behaviours of the timed system as graphs, and interpreting these graphs on tree terms by showing a bound on their tree-width.  ...  The authors thank Vincent Jugé for insightful discussions on the MSO definability of realizability of TC words.  ...  Whereas, ACC(3, 6) = ff and d(3, 6) = 2 = D(3, 6) are both strict modulo-M under-approximations of the time elapsed ts(6) − ts(3) = 6.  ... 
arXiv:1707.02297v1 fatcat:mor6z5kosrcsdoxisju5gkeiwm
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