Algorithms and Computations: 10th International Symposium, by Alok Aggarwal, C. Pandu Rangan

By Alok Aggarwal, C. Pandu Rangan

Th This quantity includes the complaints of the ten ISAAC convention (Tenth - nual overseas Symposium on Algorithms And Computation) held in Ch- nai, India. This year's convention attracted seventy one submissions from as many as 17 di erent nations. every one submission used to be reviewed by means of at the very least 3 autonomous referees. After a week-long electronic mail dialogue, this system committee agreed to incorporate forty papers within the convention software. The excessive recognition fee is obviously a sign of the standard of the papers acquired. We thank this system c- mittee participants and the reviewers for his or her honest e orts. We have been lucky to have 3 invited audio system this yr, supplying for a truly beautiful application: Kurt Mehlhorn (MPI, Saarbruck ¨ en, Germany), Eva T- dos (Cornell college, U.S.A.), and Kokichi Sugihara (Univ. of Tokyo, Japan). in addition, the convention used to be preceded through an instructional on a state-of-the-art sector, net Algorithmics by means of Monika Henzinger (Compaq structures learn heart, Palo Alto, united states) as a joint occasion with FST&TCS ninety nine (Foundations of software program Te- nology and Theoretical laptop technological know-how, December 13-15, 1999, Chennai).Asa publish convention occasion, a two-day workshop on Approximate Algorithms by way of R.Ravi (CMU, usa) and Naveen Garg (IIT, Delhi) used to be geared up. We thank the entire in- ted audio system and specified occasion audio system for agreeing to take part in ISAAC'99.

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The proofs in this extended abstract are only sketched. Multiple Spin-Block Decisions 2 29 Decomposition of the Multiple Spin-Block Problem The only relevant information from the input is a staircase function from the reals (time) into the nonnegative integers (number of running jobs), called the workload function f . Note that f = 0 outside the finite interval from the arrival of the first job until completion of the last job. Similarly, the outcome of a deletion algorithm is a function g ≥ f indicating the number of threads at each time.

Knuth, D. , “Optimum Binary Search Trees”, Acta Informatica 1(1) (1971), 14–25. 9. Overmars, M. , “The Design of Dynamic Data Structures”, Lecture Notes on Computer Science 156, Springer Verlag, 1983. 10. , “Self Adjusting k-ary Search Trees”, J. of Algorithms 19(1) (1995), 25–44. 11. Sleator, D. , Tarjan, R. , “Self Adjusting Binary Search Trees”, J. M. 32(3) (1985), 652–686. 12. Sleator, D. , Tarjan, R. , “Amortized Efficiency of List Updates and Paging Rules”, C. M. 28(2) (1985), 202–208. 13.

In an optimal R with denominator n we have tn = 1, and r = 1 + n−1 maxk ((sk + k)/tk − k). Proof. Assuming tn > 1, let u be that index with tu ≤ 1 < tu+1 . The tk , k > u do not appear in the rk , k ≤ u, and the rk , k > u are monotone increasing in all ti . Hence for any fixed t1 , . . , tu we get minimum r if tu+1 = . . = tn instead of the given values. This shows tn ≤ 1. We conclude that rk = ((sk + k)/tk + n − k)/n for all k. Now assume tn < 1. If we multiply all ti by the same factor a > 1 then all rk decrease.

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