By Sue Whitesides (auth.), Peter Eades, Tadao Takaoka (eds.)
This publication constitutes the refereed complaints of the twelfth foreign convention on Algorithms and Computation, ISAAC 2001, held in Christchurch, New Zealand in December 2001.
The sixty two revised complete papers offered including 3 invited papers have been rigorously reviewed and chosen from a complete of 124 submissions. The papers are equipped in topical sections on combinatorial iteration and optimization, parallel and disbursed algorithms, graph drawing and algorithms, computational geometry, computational complexity and cryptology, automata and formal languages, computational biology and string matching, and algorithms and knowledge constructions.
Read Online or Download Algorithms and Computation: 12th International Symposium, ISAAC 2001 Christchurch, New Zealand, December 19–21, 2001 Proceedings PDF
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Additional info for Algorithms and Computation: 12th International Symposium, ISAAC 2001 Christchurch, New Zealand, December 19–21, 2001 Proceedings
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5]). The update works as follows. Assume we join clusters i and j. For a cluster k diﬀerent from i and j, the distance to the new cluster is the maximum of the distances to i and j. Hence for all clusters diﬀerent from i and j, we have two deletions and one insert to the priority-queue. For the new cluster, we compute the distance to a point k as the maximum of the distances to i and j and build a new priority-queue of size at most n. All operations can be performed in O(n log n) in total. The main problem for our application is the space requirement of Θ(n2 ), which we can not aﬀord as we consider millions of input points.
In Figure 1, we show the time that the algorithm needs in order to make a certain number of unions. In order to join the ﬁrst two points into a cluster, all pairs of distances have to be computed. Afterwards, the necessary distances are stored in the small priority queues and the joins were performed quite fast. When the small priority queues get empty, we have to reﬁll them which increases the average time for a join of two clusters. Although, the number of reﬁlls of the priority queues does not increase more in the last iterations, the re-computation of distances becomes expensive, as we have to compute the distance of each node in a cluster to all other nodes.