# Collision-Free Routing Problem with Restricted L-Path.

## Date of Submission

December 2018

## Date of Award

Winter 12-12-2019

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

## Subject Name

Computer Science

## Department

Advance Computing and Microelectronics Unit (ACMU-Kolkata)

## Supervisor

Roy, Sasanka (ACMU-Kolkata; ISI)

## Abstract (Summary of the Work)

We consider a variant of colision-free routing problem CRP. In this problem, we are given set C of n vehicles which are moving in a plane along a predefined directed rectiline ar path. Our objective (CRP) is to find the maximum number of vehicles that can move without collision. CRP is shown to be NP-Hard by A jaykumar et al. |1|. It was also sh own that the approximation of this problem is as hard as Maximum Independent Set problem (MIS) even if the paths between a pair of vehicles intersec ts at most on ce. We study the constrained version CCRP of CRP in which each vehicle e is allowed to move in a directed L-Shaped Path. We prove CCRP is NP-Hard by a reduction from MIS in L-graphs, which was proved to be NP-Hard even for unit L-graph by Lahiri, Mukherjee, and Subra- manian 2|. S multaneously, we show that any CCRP can be partitioned into collection Lof L-graphs such that CCRP red uces to a problem of finding MIS in L-graph for each partition in C. Thus we show that any algorit hm, that can prod uce a B-approximation for L-graph, would produ ce a 3-approximation for CCRP. We show that unit L-graphs intersected by an axis-parallel line is Co- comparable. For this problem, we propose an algorithm for finding MIS that runs in O(n2) time and uses O(n2) space. As a corollary, we get a 2-approximation algorithm for finding MIS of unit L-graph that runs in O(n?) time and uses 0(n) space.

## Control Number

ISI-DISS-2018-397

## Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

## DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/6963

## Recommended Citation

Kumar, Jammigumpula, "Collision-Free Routing Problem with Restricted L-Path." (2019). *Master’s Dissertations*. 307.

https://digitalcommons.isical.ac.in/masters-dissertations/307

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843343