Related papers: Map enumeration from a dynamical perspective
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…
We present an unexpected connection between two map enumeration problems. The first one consists in counting planar maps with a boundary of prescribed length. The second one consists in counting planar maps with two points at a prescribed…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
Branched covers of the complex projective line ramified over $0,1$ and $\infty$ (Grothendieck's {\em dessins d'enfant}) of fixed genus and degree are effectively enumerated. More precisely, branched covers of a given ramification profile…
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…
Knowledge graphs have emerged to be promising datastore candidates for context augmentation during Retrieval Augmented Generation (RAG). As a result, techniques in graph representation learning have been simultaneously explored alongside…
In the last decade, subgraph detection and enumeration have emerged as a central problem in distributed graph algorithms. This is largely due to the theoretical challenges and practical applications of these problems. In this paper, we…
We initiate the study of enumerating linear subspaces of alternating matrices over finite fields with explicit coordinates. We postulate that this study can be viewed as a linear algebraic analogue of the classical topic of enumerating…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
In this article we introduce Graph Generation, an enhanced Column Generation (CG) algorithm for solving expanded linear programming relaxations of mixed integer linear programs. To apply Graph Generation, we must be able to map any given…
Map construction methods automatically produce and/or update road network datasets using vehicle tracking data. Enabled by the ubiquitous generation of georeferenced tracking data, there has been a recent surge in map construction…
This work is a follow-up of the article [Proc.\ London Math.\ Soc.\ 119(2):358--378, 2019], where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the…
Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
In this purely experimental work we try to represent the set of plane maps with 3 vertices and 3 faces as a bipartite ribbon graph. In particular, this construction allows one to estimate the genus of the initial set.
This paper presents a new anytime algorithm for the marginal MAP problem in graphical models. The algorithm is described in detail, its complexity and convergence rate are studied, and relations to previous theoretical results for the…
We consider the problem of enumeration of maps from plurifibered varieties.