Multiple-Size Divide-and-Conquer Recurrences* Ming-Yang Kao t Department of Computer Science Duke University Durham, N C 27708 U.S.A. kao~cs.duke.edu Introduction This note reports a tight asymptotic solution to the following recurrence on all positive integers n: T(n) = c-n - log o n + E,~I ai.T(Fbi-n]) for n _> no, 0 < T(n) < d for n < no, where ¢ (1) (2) ~ >_ 0,/~_> 0, c > 0, d > 0, ¢ k is a positive integer, ¢ ai>0andl>bi>0fori=l,...,k, ¢ no ~> marx,_- 1 --- /r 1 1--bi " Since no _> max,= 1 1---~,1 Fbi.nl < n - 1 for all b~ and n >_ no. Thus, the T(n) term on the left-hand side of (1) is defined on T-terms with smaller n, and (2) properly specifies the initial values of T. A special case of this recurrence, namely, k = 1, is discussed in [2, 5] and standard textbooks on algorithms and is used extensively to analyze divide-and-conquer strategies [1, 4]. A specific recurrence with k - 2 is used to analyze a divide-and-conquer algorithm for selecting a key with a given rank [1, 3, 4]. *A version of this work appeared in Proceedings of
End of preview. The entire article is 3 pages. To view the full-text, please rent this article to continue.
/lp/association-for-computing-machinery/multiple-size-divide-and-conquer-recurrences-1TAgJnBUMN
Welcome to DeepDyve! Rent Premier Research Articles and Save Up to 90%
Multiple-size divide-and-conquer recurrences
Kao, Ming-Yang
Follow ACM SIGACT News
, Volume 28 (2)
Association for Computing Machinery – Jun 1, 1997
More Info
More Like This Article
View All dataSource[]=actageo&dataSource[]=aspet&dataSource[]=aaos&dataSource[]=aacc&dataSource[]=aacr&dataSource[]=aea&dataSource[]=aip&dataSource[]=ajnr&dataSource[]=ams&dataSource[]=aps_physical&dataSource[]=appi_book&dataSource[]=appi_journal&dataSource[]=apha&dataSource[]=asip&dataSource[]=asm&dataSource[]=asn&dataSource[]=aspb&dataSource[]=avs&dataSource[]=annual_reviews&dataSource[]=arxiv&dataSource[]=acm&dataSource[]=berghahn&dataSource[]=cabi&dataSource[]=clinical_trials&dataSource[]=dailymed&dataSource[]=degruyter&dataSource[]=du_press&dataSource[]=esa&dataSource[]=eu_press&dataSource[]=elsevier&dataSource[]=emerald&dataSource[]=ejtr&dataSource[]=emea&dataSource[]=epo&dataSource[]=faseb&dataSource[]=gsa&dataSource[]=health_affairs&dataSource[]=hindawi&dataSource[]=imanager&dataSource[]=imedpub&dataSource[]=informa_healthcare&dataSource[]=informs&dataSource[]=iop&dataSource[]=iucr&dataSource[]=iospress&dataSource[]=jbjs&dataSource[]=leftcoast&dataSource[]=lu_press&dataSource[]=mesharpe&dataSource[]=mary_ann_liebert&dataSource[]=medline&dataSource[]=mit_press&dataSource[]=nature&dataSource[]=oxford&dataSource[]=pier_professional&dataSource[]=pnas&dataSource[]=portlandpress&dataSource[]=psyc_articles&dataSource[]=psyc_books&dataSource[]=psyc_critiques&dataSource[]=plos_journal&dataSource[]=pubmed_central&dataSource[]=rsna&dataSource[]=rockefeller&dataSource[]=rcn&dataSource[]=ria&dataSource[]=rsc&dataSource[]=sage&dataSource[]=spie&dataSource[]=springer_journal&dataSource[]=springer&dataSource[]=taylor_francis&dataSource[]=aps&dataSource[]=the_scientist&dataSource[]=uc_press&dataSource[]=uspto_abstract&dataSource[]=wiley&dataSource[]=pct
© 2012 DeepDyve, Inc. All rights reserved.
Terms of Service | Privacy Policy
