# Algorithm Theory - SWAT 2000: 7th Scandinavian Workshop on by Mikkel Thorup, David R. Karger (auth.)

By Mikkel Thorup, David R. Karger (auth.)

This e-book constitutes the refereed court cases of the seventh Scandinavian Workshop on set of rules idea, SWAT 2000, held in Bergen, Norway, in July 2000.

The forty three revised complete papers provided including three invited contributions have been conscientiously reviewed and chosen from a complete of a hundred and five submissions. The papers are prepared in sections on information buildings, dynamic walls, graph algorithms, on-line algorithms, approximation algorithms, matchings, community layout, computational geometry, strings and set of rules engineering, exterior reminiscence algorithms, optimization, and allotted and fault-tolerant computing.

**Read or Download Algorithm Theory - SWAT 2000: 7th Scandinavian Workshop on Algorithm Theory Bergen, Norway, July 5–7, 2000 Proceedings PDF**

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**Extra info for Algorithm Theory - SWAT 2000: 7th Scandinavian Workshop on Algorithm Theory Bergen, Norway, July 5–7, 2000 Proceedings**

**Sample text**

All pairing heap operations take constant actual time, except extractmin and delete, which take time linear in the number of children of the node to be removed. For the purposes of implementation, pairing heaps are stored as a binary tree using the leftmost child, right sibling correspondence. Unless otherwise stated, the standard tree terminology will refer to the general tree representation. 3 Constant Amortized Time Insert and Zero Amortized Time Meld in Pairing Heaps We claim that in a pairing heap the amortized runtime of find-min, make-heap, and insert is O(1), meld is O(0) and decrease-key, delete and extract-min is O(log n).

Without update operations) can have constant query time and linear space consumption. Allowing randomization, the FKS static dictionary can be made dynamic, supporting insertions and deletions in amortized expected constant time [4]. e. probability at least 1 − n−c , where c is any constant of our choice). A simpler dictionary with the same properties was later developed [3]. As for randomized dictionaries, this leaves very little to be improved. Without a source of random bits, the task of simultaneously achieving fast updates and constant query time seems considerably harder.

Instead, we use persistent balanced search trees [6], which support updates and queries in time O(log t) for a sequence of trees of size at most t. One technicality is that many instances of the algorithm finding distinguishing bits have to run at the same time and must produce well separated bit positions. However, since positions are chosen one by one, this poses no problem. In addition to what is done in the amortized case, the worst-case deletion algorithm inserts two elements of S in a new dictionary.