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

2018
*
arXiv
*
pre-print

We consider the

arXiv:1803.05718v2
fatcat:kyhf3ahwvjbhhk7nrn7yv2fjxa
*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*. ...##
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Graph-transformation verification using monadic second-order logic

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

doi:10.1145/2003476.2003482
dblp:conf/ppdp/InabaHHKN11
fatcat:p5sehv2ycnfazp24dxxz4w3sxm
*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. ...##
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Multi-Searcher Optimization for the Optimal Energy Dispatch of Combined Heat and Power-Thermal-Wind-Photovoltaic Systems

2019
*
Applied Sciences
*

The available power of wind turbine (WT) units and photovoltaic (PV) units is

doi:10.3390/app9030537
fatcat:istfvqbw4rfbdc6m2suom7rbqy
*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. ...##
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Practical algorithms for MSO model-checking on tree-decomposable graphs

2014
*
Computer Science Review
*

A celebrated theorem in this area by Courcelle states that any

doi:10.1016/j.cosrev.2014.08.001
fatcat:4eogxn65frdy5hr7syli5qjd5m
*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*. ...##
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Extension Complexity, MSO Logic, and Treewidth
[article]

2020
*
arXiv
*
pre-print

We consider the convex hull P_φ(G) of all satisfying assignments of a given

arXiv:1507.04907v9
fatcat:3z3rpkfwbvffhji6vtdbqkfhpm
*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 ...##
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Extension Complexity, MSO Logic, and Treewidth

2019
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Discrete Mathematics & Theoretical Computer Science
*

We consider the convex hull $P_{\varphi}(G)$ of all satisfying assignments of a given

doi:10.23638/dmtcs-22-4-8
fatcat:bt354gly3veejgspc4qamj6ixq
*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 ...##
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A logic-based algorithmic meta-theorem for mim-width
[article]

2022
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arXiv
*
pre-print

This results in algorithms with tight run times

arXiv:2202.13335v1
fatcat:nft3dmarxnczdbkhuo4n4wnmoy
*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). ...##
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Width Parameters Beyond Tree-width and their Applications

2007
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Computer journal
*

Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on

doi:10.1093/comjnl/bxm052
fatcat:n4nbasuvubc5lkajkskqk22fey
*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. ...##
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On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic
[article]

2009
*
arXiv
*
pre-print

Using our results from the first part of our work we establish a strong lower bound for tractability of

arXiv:0907.3076v1
fatcat:ajfgzk6oqregpiwfrvvkec3viu
*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 ...##
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A Generalization of the Łoś-Tarski Preservation Theorem - Dissertation Summary
[article]

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

arXiv:1811.01014v1
fatcat:vurmh3kcrbgtve7yp6lqngflpy
*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. ...##
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Analyzing Timed Systems Using Tree Automata
[article]

2017
*
arXiv
*
pre-print

The main idea is to consider timed behaviors as

arXiv:1604.08443v3
fatcat:hsgq6ornprah3hl6h34jac65aa
*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. ...##
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Diagnosis for Control and Decision Support for Autonomous Vehicles
[chapter]

2016
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Complex Systems
*

An

doi:10.1007/978-3-319-28860-4_1
fatcat:ud2thn5bpfdlziauier6rd7g4a
*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. ...##
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Space complexity: what makes planar graphs special?

2013
*
Bulletin of the European Association for Theoretical Computer Science
*

There are several new efficient algorithms for a variety of

dblp:journals/eatcs/DattaK13
fatcat:errya5hbabeg5bh2qph5yobtiy
*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. ...##
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Linear kernels for edge deletion problems to immersion-closed graph classes
[article]

2016
*
arXiv
*
pre-print

We prove that whenever all

arXiv:1609.07780v1
fatcat:uzgswbuyhvacrirs5e75kcapnu
*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*. ...##
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Towards an Efficient Tree Automata based technique for Timed Systems
[article]

2017
*
arXiv
*
pre-print

Our technique consists of modeling the behaviours of the timed system as

arXiv:1707.02297v1
fatcat:mor6z5kosrcsdoxisju5gkeiwm
*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. ...
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