Faster parameterized algorithms for minor containment
TL;DR: This work improves the dependence on k of Hicks' result by showing that checking if H is a minor of G can be done in time O, and sets up an approach based on a combinatorial object called rooted packing, which captures the properties of the subgraphs of H that the authors seek in their dynamic programming algorithm.
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About: This article is published in Theoretical Computer Science. The article was published on 01 Nov 2011. and is currently open access. The article focuses on the topics: Graph minor & Branch-decomposition.
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Citations
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A practical heuristic for finding graph minors
TL;DR: A heuristic algorithm for finding a graph H as a minor of a graph G that is practical for sparse $G$ and $H$ with hundreds of vertices is presented.
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Discrete optimization using quantum annealing on sparse Ising models
TL;DR: A way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware are proposed.
Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions
Eun Jung Kim,Alexander Langer,Christophe Paul,Felix Reidl,Peter Rossmanith,Ignasi Sau,Somnath Sikdar +6 more
TL;DR: It is shown that any parameterized graph problem (with parameter k) that has a finite integer index and such that Yes-instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H.
Adiabatic quantum programming: minor embedding with hard faults
TL;DR: In this paper, the authors present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells, which can be extended with fabric growth while scaling linearly in time and quadratically in footprint.
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Embedding Algorithms for Quantum Annealers with Chimera and Pegasus Connection Topologies
Stefanie Zbinden,Andreas Bärtschi,Hristo Nikolov Djidjev,Stephan Eidenbenz +3 more
- 22 Jun 2020
TL;DR: In this article, two new algorithms, Spring-Based MinorMiner (SPMM) and Clique-Based minorminer (CLMM), were proposed to produce an embedding of the input graph on a host graph that models the topology of a quantum computing device.
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Analytic Combinatorics
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TL;DR: This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.
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