Algorithms and Data Structures: 6th International Workshop, by Artur Andrzejak, Komei Fukuda (auth.), Frank Dehne,

By Artur Andrzejak, Komei Fukuda (auth.), Frank Dehne, Jörg-Rüdiger Sack, Arvind Gupta, Roberto Tamassia (eds.)

The papers during this quantity have been awarded on the 6th Workshop on Algorithms and information constructions (WADS '99). The workshop happened August eleven - 14, 1999, in Vancouver, Canada. The workshop alternates with the Scandinavian Workshop on Algorithms conception (SWAT), carrying on with the culture of SWAT and WADS beginning with SWAT'88 and WADS'89. according to 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 offer 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 specific our appreciation to the six plenary academics who accredited our invitation to talk, to the entire authors who submitted papers to W ADS'99, and to the Pacific Institute for Mathematical Sciences for his or her sponsorship. eventually, we wish to precise our gratitude to the entire those that 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 application Committee Chairs: F. Dehne, A. Gupta, J.-R. Sack, R. Tamassia software 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 info for Algorithms and Data Structures: 6th International Workshop, WADS’99 Vancouver, Canada, August 11–14, 1999 Proceedings

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1. Each RRi(S, T l , c) contains one unique reachable region, c E C. 2. Let 'I' E RR i (5, Tj,c) with typ,e(r) = 1. Then, RR(r, c) = r. 3. Let 'I' E RRi(S, Yj,c) with type(r) = 2 and r E {+c, -c}. Then, RR(r, e) :::) 'I' and type(RR(r, c)) = 1. Property 6. In case that a e-oriented reachable region has a c-oriented forward extension from tube Tk to tube T j , then at most one c-oriented reachable region in each tube Tk+l, ... , Tj-l has a forward extension into Tj: Lemma 3. Let F£(RRi(5, T k , e), T k , Tj, c) :#: 0, k < j < n.

Property 6. In case that a e-oriented reachable region has a c-oriented forward extension from tube Tk to tube T j , then at most one c-oriented reachable region in each tube Tk+l, ... , Tj-l has a forward extension into Tj: Lemma 3. Let F£(RRi(5, T k , e), T k , Tj, c) :#: 0, k < j < n. Then, F£(RRi(S, k < I < j. Tl, c), Tl, T;, c) contains at most one reachable region for any I, Th~orem 3. RRi (S, Tj , c) contains at most 3jf 2a:;n HICI-l) disjoint reachable regIOns. Sketch of the proof: The number of reachable regions in RRi (S, T j , e) is the sum of the reachable regions in: (1) nn(nni(S, Tj )\nni(S, Tj, e), e), (2) ut:~ F£((nni(S, Tk)\nni(S, Tk, e)), Tk, Tj,e), (3) nn(nni(S, Tj,e),e), and (4) ut:~F£(nni(S,Tk,C),Tk,Tj,e), By induction on j we show that the sum of all D reachable regions is bounded by 3jf 2a:;n HICI - 1).

Whenever two data blocks become empty, the younger one is deallocated; and whenever the index block becomes less than a quarter full, it is halved in size. To find the block containing a specified element, we find the superblock containing it by computing the leading I-bit, then the appropriate data block within the superblock, and finally the element within that data block. Note that the data structure also has a constant-size block, which stores the number of elements (n), the number of superblocks (s), the number of nonempty data blocks (d), the number of empty data blocks (which is always 0 or 1), and the size and occupancy of the last nonempty data block, the last superblock, and the index block.

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