Related papers: A new transfer-matrix algorithm for exact enumerat…
Walks in a directed graph can be given a partially ordered structure that extends to possibly unconnected objects, called hikes. Studying the incidence algebra on this poset reveals unsuspected relations between walks and self-avoiding…
We give exact relations for a number of amplitude combinations that occur in the study of self-avoiding walks, polygons and lattice trails. In particular, we elucidate the lattice-dependent factors which occur in those combinations which…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…
Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some…
In this paper, we provide a family of dynamic programming based algorithms to sample nearly-shortest self avoiding walks between two points of the integer lattice $\mathbb{Z}^2$. We show that if the shortest path of between two points has…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
We investigate quantum backtracking algorithms of a type previously introduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of unknown structure, and in certain cases exponentially outperform classical procedures (such as…
We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the number of vertices goes to infinity. Central limit theorems for…
We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. As we demonstrate, the numerical data for these problems demonstrates some surprising behavior.…
The collapse transition of an isolated polymer has been modelled by many different approaches, including lattice models based on self-avoiding walks and self-avoiding trails. In two dimensions, previous simulations of kinetic growth trails,…
We study self-avoiding walks on restricted square lattices, more precisely on the lattice strips $\mathbb{Z} \times \{-1,0,1\}$ and $\mathbb{Z}\times \{-1,0,1,2\}$. We obtain the value of the connective constant for the $\mathbb{Z} \times…
This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state…
Several algorithms have been used for mass transfer between particles undergoing advective and macro-dispersive random walks. The mass transfer between particles is required for general reactions on, and among, particles. The mass transfer…
We study two simple modifications of self-avoiding polygons. Osculating polygons are a super-set in which we allow the perimeter of the polygon to touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest neighbour…
Autonomous robots require online trajectory planning capability to operate in the real world. Efficient offline trajectory planning methods already exist, but are computationally demanding, preventing their use online. In this paper, we…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Green's function for the process equals 1/x^2. If the process is modified so as to be weakly self-repelling, it was shown that…
We illustrate the application of the matrix-transfer method for a number of enumeration problems concerning the party game Silent Circles, Hamiltonian cycles in the antiprism graphs, and simple paths and cycles of a fixed length in…
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…