Related papers: Polynomial braid combing
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
We define an action of Artin's braid group on a finite dimensional algebra.
When the boundary of a familiar object is shown by a series of isolated dots, humans can often recognize the object with ease. This ability can be sustained with addition of distracting dots around the object. However, such capability has…
Cobordism groups and cut-and-paste groups of manifolds arise from imposing two different relations on the monoid of manifolds under disjoint union. By imposing both relations simultaneously, a cobordism cut and paste group…
The group described in this paper appeared while studying fundamental groups of complements of branch curves. It turned out that a certain quotient of the braid group acts on those fundamental groups and studying this action is essential…
We introduce and develop a language of semigroups over the braid groups for a study of braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application we give a new proof of Orevkov's theorem on…
A PROB is a "product and braid" category. Such categories can be used to encode the structure borne by an object in a braided monoidal category. In this paper we provide PROBs whose categories of algebras in a braided monoidal category are…
Similar pictures appear in various branches of mathematics. Sometimes this similarity gives rise to deep theorems. Mentioning such a similarity between hexagonal tilings, cubes in 3-space, configurations of lines and braid groups, we prove…
The Calisson puzzle is a tiling puzzle in which one must tile a triangular grid inside a hexagon with lozenges, under the constraint that certain prescribed edges remain tile boundaries and that adjacent lozenges along these edges have…
Let M be a compact, connected non-orientable surface without boundary and of genus g greater than or equal to 3. We investigate the pure braid groups P_n(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact…
In a graph, a perfect matching cut is an edge cut that is a perfect matching. Perfect Matching Cut (PMC) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and…
A disconnected cut of a connected graph is a vertex cut that itself also induces a disconnected subgraph. The decision problem whether a graph has a disconnected cut is called Disconnected Cut. This problem is closely related to several…
The question of whether there is a logic that captures polynomial time was formulated by Yuri Gurevich in 1988. It is still wide open and regarded as one of the main open problems in finite model theory and database theory. Partial results…
The clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for…
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
This document is a practical guide to computations using an automatic structure for the mapping class group of a once-punctured, oriented surface $S$. We describe a quadratic time algorithm for the word problem in this group, which can be…
The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…
We propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted graph…