Preserving order in a forest in less than logarithmic time

  title={Preserving order in a forest in less than logarithmic time},
  author={Peter van Emde Boas},
  journal={16th Annual Symposium on Foundations of Computer Science (sfcs 1975)},
  • P. Boas
  • Published 13 October 1975
  • Computer Science
  • 16th Annual Symposium on Foundations of Computer Science (sfcs 1975)

A Survey on Priority Queues

  • G. Brodal
  • Medicine
    Space-Efficient Data Structures, Streams, and Algorithms
  • 2013
This paper tries to list some of the directions research on priority queues has taken in the last 50 years.

Range-Restricted Mergeable Priority Queues

  • J. Bright
  • Mathematics, Computer Science
    Inf. Process. Lett.
  • 1993

Advanced Data Structures Spring Semester, 1993/4 Lectures 4-5: Stratiied Trees

  • Computer Science
The Stratiied{Tree is a data structure, based upon a hierarchically decomposed tree, which enables us to manipulate, for example, a queue with priorities that are selected from the interval f1, which works with a worst case processing time of O(log log n) per instruction.

Tight(er) worst-case bounds on dynamic searching and priority queues

A novel technique is introduced for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures and optimal bounds for these structures are presented.

Log-Logarithmic Worst-Case Range Queries are Possible in Space Theta(N)

  • D. Willard
  • Computer Science, Mathematics
    Inf. Process. Lett.
  • 1983

Faster deterministic sorting and priority queues in linear space

  • M. Thorup
  • Computer Science, Mathematics
    SODA '98
  • 1998
The techniques give a deterministic linear space priority queue supporting insert and delete in O((log logn) 2 ) amortized time and nd-min in constant time and can be implemented using addition, shift, and bit-wise boolean operations.

Improved Data Structures for Predecessor Queries in Integer Sets

We consider the problem of maintaining a dynamic ordered set of n integers in the range 0 : :2 w ?1, under the operations of insertion, deletion and predecessor queries, on a unit-cost RAM with a

An Experimental Evaluation of Hybrid Data Structures for Searching

This work performs an experimental evaluation of hybrid data structures in the context of maintaining a dynamic ordered set whose items have integer or floating-point keys, and demonstrates clear speedups over library implementations of search trees, both for predecessor queries and updates.

Deferred-query : An efficient approach for some problems on interval graphs

This paper introduces the idea of a deferred-query approach to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit, and maximum matching

Design of data structures for mergeable trees

A novel variant of the problem of efficiently maintaining dynamic rooted trees, which allows an operation that merges two tree paths, is considered and a data structure is developed that supports merges and all other standard tree operations in O(log2 n) amortized time on an n-node forest.



Set Merging Algorithms

This paper considers the problem of merging sets formed from a total of n items in such a way that at any time, the name of a set containing a given item can be ascertained. Two algorithms using

Efficiency of Equivalence Algorithms

  • M. Fischer
  • Mathematics
    Complexity of Computer Computations
  • 1972
The equivalence problem is to determine the finest partition on a set that is consistent with a sequence of assertions of the form “x ≡ y”. A strategy for doing this on a computer processes the

The Design and Analysis of Computer Algorithms

This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.

Edge-disjoint spanning trees, dominators, and depth-first search.

This paper presents an algorithm for finding two edge-disjoint spanning trees rooted at a fixed vertex of a directed graph. The algorithm uses depth-first search, an efficient method for computing

On finding lowest common ancestors in trees

The first on line algorithm is applied to a problem in code optimization, that of computing immediate dominators in a reducible flow graph and it is shown how this computation can be performed in O(n log n) steps.

Efficient Generation of Optimal Prefix Code: Equiprobable Words Using Unequal Cost Letters

An algorithm for constructing an optimal prefix code of n probable words over r unequal cost coding letters is given and the number of steps required is O(r.n.log n), if a heap data structure is used.

Efficiency of a Good But Not Linear Set Union Algorithm

It is shown that, if t(m, n) is seen as the maximum time reqmred by a sequence of m > n FINDs and n -- 1 intermixed UNIONs, then kima(m), n is shown to be related to a functional inverse of Ackermann's functmn and as very slow-growing.

n log log n) On-Line Algorithm for the Insert-Extract Min Problem 3 Rep

  • of Compo Sci., Cornell Univ
  • 1485