Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


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).


ProQuest Collection ID:

Control Number


Creative Commons License

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


Included in

Mathematics Commons