相关论文: Average path length for Sierpinski pentagon

Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage $n$ is a non-negative integer. For any given vertex $x$ of SG(n), we derive rigorously the probability distribution of the degree $j \in \{1,2,3,4\}$ at the…

We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP)…

For a given polygonal region $P$, the Lawn Mowing Problem (LMP) asks for a shortest tour $T$ that gets within Euclidean distance 1 of every point in $P$; this is equivalent to computing a shortest tour for a unit-disk cutter $C$ that covers…

DPillar has recently been proposed as a server-centric datacenter network and is combinatorially related to (but distinct from) the well-known wrapped butterfly network. We explain the relationship between DPillar and the wrapped butterfly…

We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the…

The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with…

In a hyperbolic polygon any finite collection of closed billiard trajectories can be assigned an average length function. In this paper, we consider the average length of the collection of cyclically related closed billiard trajectories in…

A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…

In recent decades, much attention has been focused on the topic of optimal paths in weighted networks due to its broad scientific interest and technological applications. In this work we revisit the problem of the optimal path between two…

The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and maximum flow algorithms. Since being introduced by Edmonds and Karp in 1972, it has been widely applied in many different settings.…

Hyperbolic tilings are natural infinite planar graphs where each vertex has degree $q$ and each face has $p$ edges for some $\frac1p+\frac1q<\frac12$. We study the structure of shortest paths in such graphs. We show that given a set of $n$…

Continuous 2-dimensional space is often discretized by considering a mesh of weighted cells. In this work we study how well a weighted mesh approximates the space, with respect to shortest paths. We consider a shortest path $…

Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…

This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an…

Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…

We study the distribution of maximal-chain lengths between two elements of a causal set and its relationship with the embeddability of the causal set in a region of flat spacetime. We start with causal sets obtained from uniformly…

A $(1+\epsilon)$-approximate distance oracle of an edge-weighted graph is a data structure that returns an approximate shortest path distance between any two query vertices up to a $(1+\epsilon)$ factor. Thorup (FOCS 2001, JACM 2004) and…

It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…

A covering path for a finite set $P$ of points in the plane is a polygonal path such that every point of $P$ lies on a segment of the path. The vertices of the path need not be at points of $P$. A covering path is plane if its segments do…