# Collision-free routing problem with restricted L-path

## Article Type

Research Article

## Publication Title

Discrete Applied Mathematics

## Abstract

Given a set of vehicles that are allowed to move in a plane along a predefined directed rectilinear path, the collision-free routing problem seeks a maximum number of vehicles that can move without collision. This problem is known to be NP-hard (Ajaykumar et al., 2016). Here we study a variant of this problem called the constrained collision-free routing problem (in short, CCRP). In this problem, each vehicle is allowed only to move in a directed L-shaped path. First, we show that CCRP is NP-hard. Further, we prove that any β-approximation algorithm for the maximum independent set problem in B1-VPG graphs would produce a β-approximation for CCRP. Also, we propose a 2-approximation algorithm for the maximum independent set problem on intersection graph of n unit-L frames (the union of a unit-length vertical and a unit-length horizontal line segment that shares an endpoint) with O(n) space and O(n2) time.

## First Page

71

## Last Page

80

## DOI

10.1016/j.dam.2021.04.013

## Publication Date

10-15-2022

## Recommended Citation

Ajay, Jammigumpula; Jana, Satyabrata; and Roy, Sasanka, "Collision-free routing problem with restricted L-path" (2022). *Journal Articles*. 2925.

https://digitalcommons.isical.ac.in/journal-articles/2925