Alternative Approach to Achieve a Solution of Derangement Problems by Dynamic Programming

10 pages•Published: March 22, 2023

Thitivatr Patanasakpinyo and Adel Sulaiman

Abstract

Derangement is one well-known problem in the filed of probability theory. An in- stance of a derangement problem contains a finite collection C of n paired objects, C = {(x1 , y1 ), ..., (xn , yn )}. The derangement problem asks how many ways to gener- ate a new collection C′ ̸= C such that for each (xi,yj) ∈ C′,i ̸= j. We propose an efficient dynamic programming algorithm that divides an instance of the derangement problem into several subproblems. During a recursive process of unrolling a subproblem, there exists a repeated procedure that allows us to make a use of a subsolution that has already been computed. We present the methodology to formulate a concept of this subproblem as well as parts of designing and analyzing an efficiency of the proposed algorithm.

Keyphrases: algorithm, derangement, dynamic programming, probability theory, recursion

In: Ajay Bandi, Mohammad Hossain and Ying Jin (editors). Proceedings of 38th International Conference on Computers and Their Applications, vol 91, pages 98-107.

Links:	https://easychair.org/publications/paper/bjP9
	https://doi.org/10.29007/1j3g

BibTeX entry

@inproceedings{CATA2023:Alternative_Approach_Achieve_Solution,
  author    = {Thitivatr Patanasakpinyo and Adel Sulaiman},
  title     = {Alternative Approach to Achieve a Solution of Derangement Problems by Dynamic Programming},
  booktitle = {Proceedings of 38th International Conference on Computers and Their Applications},
  editor    = {Ajay Bandi and Mohammad Hossain and Ying Jin},
  series    = {EPiC Series in Computing},
  volume    = {91},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/bjP9},
  doi       = {10.29007/1j3g},
  pages     = {98-107},
  year      = {2023}}

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