Date of Submission

2-28-2002

Date of Award

2-28-2003

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Sikdar, Kripasindhu (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

We investigate approximability of both maximum and minimum linear ordering problems (MAX-LOP and MIN-LOP) and several related problems such as the well known feedback set problems, acyclie subdigraph problem and several others and their variants.We show that both MAX-LOP and MIN-LOP are strongly NP-complete, and MIN- LOP, MIN-QAP(S) (a special case of minimum quadratic assignment problem) and MIN-W-FAS are equivalent with respect to strict-reduction. The strict-equivalence is also established among these problems as well as MIN-W-FVS, with weights on arcs/vertices bounded by a polynomial, and the unweighted versions of the feedback set. problems. We also show that MAX-LOP is strict-equivalent with MAX-W-SUBDAG and, with weights bounded by a polynomial, they are AP-equivalent with MAX- SUBDAG, the unweighted version of MAX-W-SUBDAG. Such equivalent problems have similar approximability properties. In particular, MIN-LOP and MIN-QAP(S) have O(log n loglog n)-approximation algorithms and they are APX-hard as MIN-W- FAS has such properties. Also MAX-LOP is APX-complete as MAX-W-SUBDAG is so and has a 2-approximation algorithm.We next concentrate primarily on LOP, and, after noting that, if PNP, there cannot exist any absolute approximation algorithm for LOP, we examine the question whether MIN-LOPEAPX. We have some evidences, though not strong, that appear to suggest that MIN-LOP and other equivalent problems may not be in APX, if PNP. In particular, we establish a connection between coordinates of extreme points of lin- ear ordering polytope and the existance of a constant-factor approximate solution of MIN-LOP which seems to suggests that we may not be able to get a constant-factor approximation algorithm for MIN-LOP via a LP-relaxation and rounding method. Sec- ondly, we show that for MIN-Subset-FAS, a generalization of MIN-FAS, there cannot exist a polynomial-time (1 - e) log n-approximation algorithm, for any e > 0, unless NP C DTIME(n lognlog logn).

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:28842860

Control Number

ISILib-TH118

Creative Commons License

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

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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