NDLI: Optimal Algorithms for Sorting Permutations with Brooms

Please wait, while we are loading the content...

Optimal Algorithms for Sorting Permutations with Brooms

Content Provider	MDPI
Author	Sadanandan, Indulekha Thekkethuruthel Chitturi, Bhadrachalam
Copyright Year	2022
Abstract	Sorting permutations with various operations has applications in genetics and computer interconnection networks where an operation is specified by its generator set. A transposition tree $T = (V, E)$ is a spanning tree over n vertices $v_{1}, v_{2}, \dots v_{n}$ . T denotes an operation in which each edge is a generator. A value assigned to a vertex is called a token or a marker. The markers on vertices u and v can be swapped only if the pair $(u, v) \in E$ . The initial configuration consists of a bijection from the set of vertices $v_{1}, v_{2}, \dots, v_{n}$ to the set of markers $(1, 2, \dots, n - 1, n)$ . The goal is to sort the initial configuration of T, i.e., an input permutation, by applying the minimum number of swaps or moves in T. Computationally tractable optimal algorithms to sort permutations are known only for a few classes of transposition trees. We study a class of transposition trees called a broom and its variation a double broom. A single broom is a tree obtained by joining the centre vertex of a star with one of the two leaf vertices of a path graph. A double broom is an extension of a single broom where the centre vertex of a second star is connected to the terminal vertex of the path in a single broom. We propose a simple and efficient algorithm to obtain an optimal swap sequence to sort permutations with the transposition tree broom and a novel optimal algorithm to sort permutations with a double broom. We also introduce a new class of trees named millipede tree and prove that $D^{}$ yields a tighter upper bound for sorting permutations with a balanced millipede tree compared to $D^{'}$ . Algorithms $D^{}$ and $D^{'}$ are designed previously.
Starting Page	220
e-ISSN	19994893
DOI	10.3390/a15070220
Journal	Algorithms
Issue Number	7
Volume Number	15
Language	English
Publisher	MDPI
Publisher Date	2022-06-21
Access Restriction	Open
Subject Keyword	Algorithms Hardware and Architecturee Sorting Permutations Transposition Trees Polynomial Time Algorithms Interconnection Networks Broom Optimal Swap Sequence Cayley Graphs
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in