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We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all…

Combinatorics · Mathematics 2011-06-10 Hidehiko Kamiya , Akimichi Takemura , Hiroaki Terao

The quadratic minimum spanning tree problem (QMSTP) is the problem of finding a spanning tree of a graph such that the total interaction cost between pairs of edges in the tree is minimized. We first show that most of the bounding…

Optimization and Control · Mathematics 2024-04-09 Renata Sotirov , Zoe Verchére

Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…

Computational Complexity · Computer Science 2015-06-01 Kitty Meeks

We show that the query containment problem for monadic datalog on finite unranked labeled trees can be solved in 2-fold exponential time when (a) considering unordered trees using the axes child and descendant, and when (b) considering…

Logic in Computer Science · Computer Science 2014-04-03 André Frochaux , Martin Grohe , Nicole Schweikardt

Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the…

Combinatorics · Mathematics 2009-03-13 Reinhard Steffens , Thorsten Theobald

The new method of the mean-field approximation is extended. An approach which enables to estimate some parameters of the transition from the isotropic state of hard sticks to the nematic ordering phase is suggested. An technique of the…

Statistical Mechanics · Physics 2018-02-14 Andrei N. Yakunin

We propose a Reinforcement Learning based approach to approximately solve the Tree Decomposition (TD) problem. TD is a combinatorial problem, which is central to the analysis of graph minor structure and computational complexity, as well as…

Machine Learning · Computer Science 2020-12-08 Taras Khakhulin , Roman Schutski , Ivan Oseledets

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…

Statistics Theory · Mathematics 2012-03-06 Piotr Zwiernik , Jim Q. Smith

Treewidth is a well-known graph invariant with multiple interesting applications in combinatorics. On the practical side, many NP-complete problems are polynomial-time (sometimes even linear-time) solvable on graphs of bounded treewidth. On…

Category Theory · Mathematics 2021-05-13 Zoltan A. Kocsis , Benjamin Merlin Bumpus

In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder woods where the number of incoming edges of each color at each vertex is balanced as much as possible. We provide a simple linear-time heuristic leading…

Data Structures and Algorithms · Computer Science 2019-08-20 Luca Castelli Aleardi

We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…

Combinatorics · Mathematics 2020-04-03 David A. Levin , Eric Ramos , Benjamin Young

We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that…

Data Structures and Algorithms · Computer Science 2007-05-23 Noga Alon , Fedor Fomin , Gregory Gutin , Michael Krivelevich , Saket Saurabh

Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…

Combinatorics · Mathematics 2013-05-14 Alexander Barvinok

The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…

Data Structures and Algorithms · Computer Science 2022-03-29 Andreas Galanis , Leslie Ann Goldberg , James Stewart

Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…

Machine Learning · Computer Science 2020-07-15 Natalia Vesselinova , Rebecca Steinert , Daniel F. Perez-Ramirez , Magnus Boman

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…

Networking and Internet Architecture · Computer Science 2018-03-14 Magnus M. Halldorsson , Guy Kortsarz , Pradipta Mitra , Tigran Tonoyan

We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit, to an analytic function of the monomer activity. We…

Mathematical Physics · Physics 2015-06-15 Diego Alberici , Pierluigi Contucci

Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…

Combinatorics · Mathematics 2013-01-11 Hidehiko Kamiya , Akimichi Takemura , Norihide Tokushige

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

Machine Learning · Computer Science 2021-02-18 Jianming Huang , Hiroyuki Kasai

A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph…

Combinatorics · Mathematics 2007-05-23 H. Tracy Hall
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