On a Few Progressive Algorithms.

Date of Submission

December 2020

Date of Award

Winter 12-12-2021

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)

The progressive algorithms are algorithms that outputs intermediate solutions which approximate the complete solution to the given problem. The user can decide whether to continue the running of the algorithm based on the error of the partial solutions. In this dissertation, we have studied few problems from the perspective of progressive algorithm. We have proposed the following: Huffman encoding: a progressive algorithm for finding optimal pre x encoding or Huffman coding. We have proved that error of the partial solution in step r is bounded by n=2r-2. Overall running time of the algorithm, we have shown, is O(n log n). Convex hull in 2D: Next, we have moved towards geometric problems. We have presented a randomized progressive algorithm for finding convex hull of the points in R2. The algorithm runs in at most log n many rounds and expected running time of each round is O(n). Convex hull in 3D: We have also extended an existing progressive algorithm for finding convex hull of the points in R2 for the point set in R3. We have proposed a procedure to have an upper bound of O(log n) for the number of rounds of the algorithm for this problem. This work uses one observation whose proof eludes us but we have compelling experimental evidence for the observation.


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:28842758

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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