By Kazuo Iwama (auth.), Tetsuo Asano (eds.)
This ebook constitutes the refereed complaints of the seventeenth foreign Symposium on Algorithms and Computation, ISAAC 2006, held in Kolkata, India in December 2006.
The seventy three revised complete papers offered have been conscientiously reviewed and chosen from 255 submissions. The papers are prepared in topical sections on algorithms and information buildings, on-line algorithms, approximation set of rules, graphs, computational geometry, computational complexity, community, optimization and biology, combinatorial optimization and quantum computing, in addition to dispensed computing and cryptography.
Read or Download Algorithms and Computation: 17th International Symposium, ISAAC 2006, Kolkata, India, December 18-20, 2006. Proceedings PDF
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Additional info for Algorithms and Computation: 17th International Symposium, ISAAC 2006, Kolkata, India, December 18-20, 2006. Proceedings
Al.  presented a single pass algorithm with O 1ε log2 εn memory if n is known. This was improved to O 1ε log εn memory, not requiring the knowledge of n by Greenwald and Khanna . In the former paper, the authors also showed a (1+ε)-approximation technique with 1 probability δ using O 1ε log2 1ε log 1−δ memory. Munro and Paterson  studied the problem under several memory restrictions but for constant memory they only gave a multi-pass algorithm for the exact median without intermediate approximation results after each pass.
The algorithm the case that at least 2t ✷ sets low to m1 , guaranteeing the claimed increase of low. Lemma 3. Algorithm 2 returns an element with distance Ω the boundary in the sorted data with t = n four markers. 1 3 n t 2 = Ω n3 to and knowing n beforehand using n Proof: The algorithm will only change low, if at least 2t larger elements are known. The symmetric holds for high, so we only have to care about pushing low and high as far as we can. The n input elements can be seen as 3t blocks with 3 nt elements each.
References 1. M. Blum, R. W. Floyd, V. R. Pratt, R. L. Rivest, and R. E. Tarjan. Time bounds for selection. J. Comput. Syst. , 7(4):448–461, 1973. 2. M. Greenwald and S. Khanna. Space-eﬃcient online computation of quantile summaries. In SIGMOD ’01: Proceedings of the 2001 ACM SIGMOD international conference on Management of data, pages 58–66, New York, NY, USA, 2001. ACM Press. 3. S. Guha and A. McGregor. Approximating quantiles and the order of the stream. In PODS, 2006. 4. S. Guha, A. McGregor, and S.