Trees with Minimum Weighted Path Length

  title={Trees with Minimum Weighted Path Length},
  author={Wojciech Rytter},
  booktitle={Handbook of Data Structures and Applications},
  • W. Rytter
  • Published in
    Handbook of Data Structures…
    7 March 2018
  • Education
Warsaw University 14. 
Dual-Pivot Quicksort and Beyond: Analysis of Multiway Partitioning and Its Practical Potential
This dissertation conducts a mathematical average-case analysis of multiway Quicksort including the important optimization to choose pivots from a sample of the input and proposes a parametric template algorithm that covers all practically relevant partitioning methods as special cases, and analytically investigates in depth what effect the parameters of the generic quicksort have on its performance.
Operations research applications of dichotomous search


The least weight subsequence problem
  • D. Hirschberg, L. Larmore
  • Mathematics, Computer Science
    26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
The least weight subsequence (LWS) problem is introduced, and is shown to be equivalent to the classic minimum path problem for directed graphs, and to be solvable in O(n log n) time generally and, for certain weight functions, in linear time.
Lopsided Trees: Analyses, Algorithms, and Applications
This paper examines three problems on lopsided trees and shows how to apply the results to the analysis of problems in data compression (Varncodes) and distributed computing.
Computing a minimum-weight k-link path in graphs with the concave Monge property
An efficient algorithm is given for finding the minimum weightk-link path between a given pair of vertices for any givenk, which can be applied to get efficient solutions for the following problems.
Parallel construction of trees with optimal weighted path length
It is shown that an optimal height restricted alphabetic tree can be constructed in O(L log n) time on a CREW PRAM using only linearly many processors, where L is an upper bound on the height of the tree.
The Optimal Alphabetic Tree Problem Revisited
The Optimal Alphabetic Binary Tree (OABT) problem is equivalent to the Optimal Binary Search Tree problem with the restriction that all data are in the leaves. The problem can be solved in O(n log n)
Binary Search Trees: Average and Worst Case Behavior
We discuss several simple strategies for constructing binary search trees. Upper and lower bounds for the average and worst case search time in trees constructed according to these strategies are
A Work-Time Trade-off in Parallel Computation of Huffman Trees and Concave Least Weight Subsequence Problem
We present a parallel algorithm for the Concave Least Weight Subsequence (CLWS) problem that exhibits the following work-time trade-off: Given a parameter p, the algorithm runs in time using p
Parallel construction of binary trees with near optimal weighted path length
Two parallel algorithms to construct binary trees with almost optimal weighted path length are presented and two sequential algorithms, anO(kn)-time algorithm which produces a tree with error at most l/nk, and anO (k2 logn)-time andn2-CREW-processor algorithm which producing a treeWith error atMost l/ nk.
A New Proof of the T-C Algorithm
Although the algorithm is simple to state, the associated proof was extremely complicated and long.
An optimal parallel minimax tree algorithm
  • D. Kirkpatrick, T. Przytycka
  • Computer Science
    Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing 1990
  • 1990
An log n time n/log n processor CREW PRAM algorithm to construct an alphabetic minimax tree is presented, which achieves optimal bounds by a combination of existing parallel techniques and a new technique, called accelerated valley filling.