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The computational complexity of dominating set problems for instances with bounded minors of constraint matrices

D.S. Malyshev, D.V. Gribanov
2018 Discrete Optimization  
We consider boolean linear programming formulations of the vertex and edge dominating set problems and prove their polynomial-time solvability for classes of graphs with constraint matrices having bounded  ...  minors in the absolute value.  ...  More generally, it would be interesting to investigate the complexity of the problems with constraint matrices having bounded minors.  ... 
doi:10.1016/j.disopt.2018.03.002 fatcat:pu36r6tcsvfebgsychxfzvg354

Polynomial SDP cuts for Optimal Power Flow

Hassan Hijazi, Carleton Coffrin, Pascal Van Hentenryck
2016 2016 Power Systems Computation Conference (PSCC)  
For the Optimal Power Flow (OPF) problem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack of scalability.  ...  As a side result, we present a formulation of Kirchhoff's Voltage Law in the SDP space and reveal the existing link between these cycle constraints and the original SDP relaxation for three dimensional  ...  Council through the ICT Centre of Excellence program.  ... 
doi:10.1109/pscc.2016.7540908 dblp:conf/pscc/HijaziCH16 fatcat:tikylatj6rccbdxd3pmtlwr2yq

Polynomial SDP Cuts for Optimal Power Flow [article]

Hassan Hijazi and Carleton Coffrin and Pascal Van Hentenryck
2015 arXiv   pre-print
As a side result, we present the first formulation of Kirchhoff's Voltage Law in the SDP space and reveal the existing link between these cycle constraints and the original SDP relaxation for three dimensional  ...  For the Optimal Power Flow (OPF) problem, the Semi-Definite Programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack of scalability.  ...  Council through the ICT Centre of Excellence program.  ... 
arXiv:1510.08107v1 fatcat:f3d6d6tmv5c63jmgdpq3l2c7tq

Adiabatic Quantum Graph Matching with Permutation Matrix Constraints

Marcel Seelbach Benkner, Vladislav Golyanik, Christian Theobalt, Michael Moeller
2020 2020 International Conference on 3D Vision (3DV)  
In this work, we address such problems with emerging quantum computing technology and propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware  ...  Despite the observed discrepancy between simulated adiabatic quantum computing and execution on real quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the  ...  This work was partially supported by the ERC Consolidator Grant 4DReply (770784).  ... 
doi:10.1109/3dv50981.2020.00068 fatcat:k7d24zhr5fbsxgtdckmkmupsce

Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [article]

Marcel Seelbach Benkner and Vladislav Golyanik and Christian Theobalt and Michael Moeller
2021 arXiv   pre-print
In this work, we address such problems with emerging quantum computing technology and propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware  ...  Despite the observed discrepancy between simulated adiabatic quantum computing and execution on real quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the  ...  This work was partially supported by the ERC Consolidator Grant 4DReply (770784).  ... 
arXiv:2107.04032v1 fatcat:goa7z4iqdvd7fmcu7xfoxyspwq

New Limits of Treewidth-based tractability in Optimization [article]

Yuri Faenza, Gonzalo Muñoz, Sebastian Pokutta
2019 arXiv   pre-print
This parameter has been used for decades for analyzing the complexity of various optimization problems and for obtaining tractable algorithms for problems where this parameter is bounded.  ...  They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.  ...  Acknowledgements Research reported in this paper was partially supported by NSF CAREER award CMMI-1452463 and by the Institute for Data Valorisation (IVADO).  ... 
arXiv:1807.02551v4 fatcat:xc5pqufrvbhe5frrehjaaquu5u

FPT-algorithms for The Shortest Lattice Vector and Integer Linear Programming Problems [article]

D. V. Gribanov
2017 arXiv   pre-print
The main parameter is the maximal absolute value of rank minors of matrices included to the problem formulation.  ...  Additionally, we present FPT-algorithms with respect to the same main parameter for the problems, when the matrices have no singular rank sub-matrices.  ...  More generally, it would be interesting to investigate the complexity of the problems with constraint matrices having bounded minors.  ... 
arXiv:1710.00321v1 fatcat:e3edvuwpprfxvhpt24c5yivoba

Algorithms for Comparability of Matrices in Partial Orders Imposed by Graph Homomorphisms [chapter]

Jiří Fiala, Daniël Paulusma, Jan Arne Telle
2005 Lecture Notes in Computer Science  
For the surjective constraint we obtain some partial complexity results.  ...  If graph G has a homomorphism of given type to graph H, then we say that the degree refinement matrix of G is smaller than that of H. This way we obtain three partial orders.  ...  For computational complexity purposes X denotes the size of the instance X (graph, matrix, etc.) in usual binary encoding of numbers.  ... 
doi:10.1007/11604686_11 fatcat:ku6pb2d3uzadlo4twtlyqr4bb4

A Spatial Branch-and-Cut Method for Nonconvex QCQP with Bounded Complex Variables [article]

Chen Chen and Alper Atamturk and Shmuel S. Oren
2017 arXiv   pre-print
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP).  ...  Closed-form bound tightening procedures are used to reduce the domain of the problem.  ...  O'Neill of the Federal Energy Regulatory Commission for the initial impetus to study conic relaxations of ACOPF, and for helpful comments in early drafts of the paper.  ... 
arXiv:1705.09057v1 fatcat:6hs6wahnfvacfpqpyd6qed6wum

A spatial branch-and-cut method for nonconvex QCQP with bounded complex variables

Chen Chen, Alper Atamtürk, Shmuel S. Oren
2016 Mathematical programming  
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP).  ...  Closed-form bound tightening procedures are used to reduce the domain of the problem.  ...  O'Neill of the Federal Energy Regulatory Commission for the initial impetus to study conic relaxations of ACOPF, and for helpful comments in early drafts of the paper.  ... 
doi:10.1007/s10107-016-1095-2 fatcat:fldfcsekkbfxnewk6rzeiynlhq

Verifying the output of quantum optimizers with ground-state energy lower bounds

Flavio Baccari, Christian Gogolin, Peter Wittek, Antonio Acín
2020 Physical Review Research  
Solving optimization problems encoded in the ground state of classical-spin systems is a focus area for quantum computing devices, providing upper bounds to the unknown solution.  ...  We consider the use of relaxations to the ground-state problem as a benchmark for the output of quantum optimizers.  ...  Thereby "worst-case complexity" is the complexity of the hardest instances within a class of families of problems of increasing size.  ... 
doi:10.1103/physrevresearch.2.043163 fatcat:czyyqjyfrnhkho2oj2gzofj4gq

NC Algorithms for Computing a Perfect Matching and a Maximum Flow in One-Crossing-Minor-Free Graphs [article]

David Eppstein, Vijay V. Vazirani
2020 arXiv   pre-print
In 1988, Vazirani gave an NC algorithm for computing the number of perfect matchings in K_3,3-minor-free graphs by building on Kasteleyn's scheme for planar graphs, and stated that this "opens up the possibility  ...  In particular, we obtain NC algorithms for the following problems in any family of graphs (or networks) with a one-crossing forbidden minor: ∙ Determining whether a given graph has a perfect matching and  ...  Acknowledgements The research of David Eppstein was supported in part by NSF grants CCF-1618301 and CCF-1616248. The research of Vijay Vazirani was supported in part by NSF grant CCF-1815901.  ... 
arXiv:1802.00084v2 fatcat:zlzad5kkynhpvjyuhjjluroh7a

Lagrangian approaches for a class of matching problems in computational biology

Nicola Yanev, Rumen Andonov, Philippe Veber, Stefan Balev
2008 Computers and Mathematics with Applications  
We consider the problem as a special case of graph matching problem. We give formal graph and integer programming models of the problem.  ...  We present experimental results on real-life instances showing the efficiency of our approaches.  ...  With the notations introduced above, the complexity of PTP(L) for a sequence of such subproblems is O(sn 2 ) plus the cost of computing matrices D i t i t+1 .  ... 
doi:10.1016/j.camwa.2006.12.103 fatcat:5toykwy555afpg3kpdi7on5wxa

Solving partial constraint satisfaction problems with tree decomposition

Arie M. C. A. Koster, Stan P. M. van Hoesel, Antoon W. J. Kolen
2002 Networks  
With the use of dominance and bounding techniques, we are able to solve small and medium-size instances of the problem to optimality and to obtain good lower bounds for large-size instances within reasonable  ...  We present a dynamic programming algorithm that solves PCSPs based on the structure (tree decomposition) of the underlying constraint graph.  ...  Acknowledgments The authors would like to thank Rudolf Müller for his suggestions which resulted in the iterative algorithm of Section 4.  ... 
doi:10.1002/net.10046 fatcat:lizexjp3xfdozpthwb6kndk2ni

Distributed Matrix Tiling Using A Hypergraph Labeling Formulation [article]

Avah Banerjee, Guoli Ding, Maxwell Reeser
2021 arXiv   pre-print
In this work we consider a theoretical model for a version of the matrix tiling problem in the setting of hypergraph labeling.  ...  Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others).  ...  , and computational complexity of the expression, etc.  ... 
arXiv:2106.15549v1 fatcat:v4hm5uoh3vastbc6xl52wsu72m
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