Recently, Aichholzer, Garćıa, Orden, and Ramos derived a remarkably improved lower bound for the number of (≤ k)-edges in an n-point set, and as an immediate corollary an improved lower bound on the rectilinear crossing number of Kn. We use simple allowable sequences to extend all their results to the more general setting of simple generalized configurations of points and slightly improve the l...

This paper proposes a comparison between rectilinear and radio-concentric networks. Indeed, those networks are often observed in urban areas, in several cities all over the world. One of the interesting properties of such networks is described by the straightness measure from graph theory, which assesses how much moving from one node to another along the network links departs from the network-i...

One form of hybrid evolutionary algorithm encodes solutions to its target problem as permutations of the problem's elements. A greedy heuristic assembles the solution a permutation represents by appending the problem's elements to the solution in the order the permutation speci es. The algorithm searches the problem's solution space by searching the space of permutations. A hybrid genetic algor...

Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the Lp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where the maximum degree is minimized. We give the best-known bounds for the maximum MST degree for ar...

We study the Minimum-Length Corridor (MLC) problem. Given a rectangular boundary partitioned into rectilinear polygons, the objective is to find a corridor of least total length. A corridor is a set of line segments each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectilinear polygons. The corridor is a tree, and must include at least ...

In this paper, a new construct called connection graph, Gc, is proposed. An efficient geometric algorithm for constructing Gc is given. We present a framework for designing a class of time and space efficient maze-running and line-search rectilinear shortest path and rectilinear minimum spanning tree algorithms based on Gc. We give several example maze-running and line-search algorithms based o...