On a Class of Board Games.

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


Advance Computing and Microelectronics Unit (ACMU-Kolkata)


Bishnu, Arijit (ACMU-Kolkata; ISI)

Abstract (Summary of the Work)

Lab-on-Chip (LOC) is a device on which several laboratory functions are integrated on a chip of very small size. LOC can detect and manipulate microorganisms by applying electric field so that they can be collected at desired locations. The manipulation step involves swapping the content of one cell with another. The aim is to separate desired microorganisms from undesired ones by collecting them in their respective receptors.In this dissertation we abstract the setting of LOC to Board Games and study their efficiency and complexity. We begin identifying the desired chips as red cells or blue cells and chips that we do not care about as black cells. The interpretation may vary depending of context. Game-0 is used to define the setting for the games we study. We give a proof that Game-0 is in PSPACE and then define Game-1 and Game-2 which are our main focus in this thesis.Game-l is NP-Complete which follows from a reduction from Rectilinear Steiner Tree problem. On approximation side, it admits a Polynomial Time Approximation Scheme (PTAS). The ideas used in these proofs are also used to study Game-1. We give an O(1+ 1/n) approximation for Game-1. For each of these games we also study their integer linear programs.


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:28843270

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.



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