By Artur Andrzejak, Komei Fukuda (auth.), Frank Dehne, Jörg-Rüdiger Sack, Arvind Gupta, Roberto Tamassia (eds.)
The papers during this quantity have been offered on the 6th Workshop on Algorithms and knowledge constructions (WADS '99). The workshop came about August eleven - 14, 1999, in Vancouver, Canada. The workshop alternates with the Scandinavian Workshop on Algorithms concept (SWAT), carrying on with the culture of SWAT and WADS beginning with SWAT'88 and WADS'89. based on this system committee's demand papers, seventy one papers have been submitted. From those submissions, this system committee chosen 32 papers for presentation on the workshop. as well as those submitted papers, this system committee invited the next researchers to provide plenary lectures on the workshop: C. Leiserson, N. Magnenat-Thalmann, M. Snir, U. Vazarani, and 1. Vitter. On behalf of this system committee, we wish to precise our appreciation to the six plenary teachers who authorized our invitation to talk, to all of the authors who submitted papers to W ADS'99, and to the Pacific Institute for Mathematical Sciences for his or her sponsorship. eventually, we want to precise our gratitude to all of the those who reviewed papers on the request of this system committee. August 1999 F. Dehne A. Gupta J.-R. Sack R. Tamassia VI convention Chair: A. Gupta software Committee Chairs: F. Dehne, A. Gupta, J.-R. Sack, R. Tamassia application Committee: A. Andersson, A. Apostolico, G. Ausiello, G. Bilardi, ok. Clarkson, R. Cleve, M. Cosnard, L. Devroye, P. Dymond, M. Farach-Colton, P. Fraigniaud, M. Goodrich, A.
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Extra resources for Algorithms and Data Structures: 6th International Workshop, WADS’99 Vancouver, Canada, August 11–14, 1999 Proceedings
Newton's method [9, pp. 274-292] is known to minimize the time for this, taking 8(log log i) time in the worst case. This prevents Read and Write from running in the desired 0(1) time bound. 2 Another approach, related to that of doubling, is to use a sequence of blocks of sizes the powers of 2, starting with 1. The obvious disadvantage of these sizes is that half the storage space is wasted when the last block is allocated and contains only one element. We notice however that the number of elements in the first k blocks is 2k - 1, so the block containing element i is llog2(1 + i)J.
This data structure implements singly resizable arrays using O( yin) extra storage in the worst case and 0(1) time per operation, on a random access machine where memory is dynamically allocated, and binary shift by k takes 0(1) time on a word of size ilog2(1 + n)l. Furthermore, if Allocate or Deallocate is called when n = no, then the next call to Allocate or Deallocate will occur after D( y'nO) operations. The space bound follows from the following lemmas. See  for proofs. Lemma 1. The number of superblocks (s) is ilog2(1 + n)l.
Write (i, x): Set the element with index i to x, £:::; i :::; u. GrowForward: Increment u, creating a new element with index u + 1. ShrinkForward: Decrement u, discarding the element with index u. GrowBackward: Decrement £, creating a new element with index £ - 1. ShrinkBackward: Increment £, discarding the element with index f- An extension to our method for singly resizable arrays supports this data type in the same optimal time and space bounds. The rest of this paper is outlined as follows.