Asymptotically optimal linear time algorithms for two-stage and three-stage flexible flow shops

2000 ◽  
Vol 47 (3) ◽  
pp. 259-268 ◽  
Author(s):  
Christos Koulamas ◽  
George J. Kyparisis
Keyword(s):  
Linear Time ◽  
Two Stage ◽  
Flow Shops ◽  
Asymptotically Optimal ◽  
Optimal Linear ◽  
Linear Time Algorithms

Efficient Web Mining for Traversal Path Patterns

Web Mining ◽  
2011 ◽  
pp. 322-338 ◽  
Author(s):  
Zhixiang Chen ◽  
Richard H. Fowler ◽  
Ada Wai-Chee Fu ◽  
Chunyue Wang
Keyword(s):  
Web Mining ◽  
Linear Time ◽  
Fundamental Problem ◽  
A Priori ◽  
Web Pages ◽  
Suffix Trees ◽  
Web Logs ◽  
Large Alphabet ◽  
Optimal Linear ◽  
Linear Time Algorithms

A maximal forward reference of a Web user is a longest consecutive sequence of Web pages visited by the user in a session without revisiting some previously visited page in the sequence. Efficient mining of frequent traversal path patterns, that is, large reference sequences of maximal forward references, from very large Web logs is a fundamental problem in Web mining. This chapter aims at designing algorithms for this problem with the best possible efficiency. First, two optimal linear time algorithms are designed for finding maximal forward references from Web logs. Second, two algorithms for mining frequent traversal path patterns are devised with the help of a fast construction of shallow generalized suffix trees over a very large alphabet. These two algorithms have respectively provable linear and sublinear time complexity, and their performances are analyzed in comparison with the a priori-like algorithms and the Ukkonen algorithm. It is shown that these two new algorithms are substantially more efficient than the a priori-like algorithms and the Ukkonen algorithm.

PLANAR UPWARD TREE DRAWINGS WITH OPTIMAL AREA

1996 ◽  
Vol 06 (03) ◽  
pp. 333-356 ◽  
Author(s):  
ASHIM GARG ◽  
MICHAEL T. GOODRICH ◽  
ROBERTO TAMASSIA
Keyword(s):  
Linear Time ◽  
Rooted Tree ◽  
Rooted Trees ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Bounded Degree ◽  
Asymptotically Optimal ◽  
Grid Drawing ◽  
Optimal Area ◽  
Linear Time Algorithms

Rooted trees are usually drawn planar and upward, i.e., without crossings and with-out any parent placed below its child. In this paper we investigate the area requirement of planar upward drawings of rooted trees. We give tight upper and lower bounds on the area of various types of drawings, and provide linear-time algorithms for constructing optimal area drawings. Let T be a bounded-degree rooted tree with N nodes. Our results are summarized as follows: • We show that T admits a planar polyline upward grid drawing with area O(N), and with width O(Nα) for any prespecified constant a such that 0<α<1. • If T is a binary tree, we show that T admits a planar orthogonal upward grid drawing with area O (N log log N). • We show that if T is ordered, it admits an O(N log N)-area planar upward grid drawing that preserves the left-to-right ordering of the children of each node. • We show that all of the above area bounds are asymptotically optimal in the worst case. • We present O(N)-time algorithms for constructing each of the above types of drawings of T with asymptotically optimal area. • We report on the experimentation of our algorithm for constructing planar polyline upward grid drawings, performed on trees with up to 24 million nodes.

scholarly journals Almost Linear Time Algorithms for Minsum k-Sink Problems on Dynamic Flow Path Networks

2021 ◽  
Author(s):  
Yuya Higashikawa ◽  
Naoki Katoh ◽  
Junichi Teruyama ◽  
Koji Watase
Keyword(s):  
Linear Time ◽  
Flow Path ◽  
Dynamic Flow ◽  
Linear Time Algorithms

scholarly journals Linear-Time Algorithms for Tree Root Problems

Algorithmica ◽  
2013 ◽  
Vol 71 (2) ◽  
pp. 471-495 ◽  
Author(s):  
Maw-Shang Chang ◽  
Ming-Tat Ko ◽  
Hsueh-I Lu
Keyword(s):  
Linear Time ◽  
Linear Time Algorithms

FAULT TOLERANT ROUTING IN HYPERCUBES AND STAR GRAPHS

1996 ◽  
Vol 06 (01) ◽  
pp. 127-136 ◽  
Author(s):  
QIAN-PING GU ◽  
SHIETUNG PENG
Keyword(s):  
Free Path ◽  
Fault Tolerant ◽  
Linear Time ◽  
Time Efficiency ◽  
Routing Problem ◽  
Star Graphs ◽  
Linear Time Algorithms ◽  
Better Than

In this paper, we give two linear time algorithms for node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn and star graphs Gn. The first algorithm, given at most n−1 arbitrary fault nodes and two non-fault nodes s and t in Hn, finds a fault-free path s→t of length at most [Formula: see text] in O(n) time, where d(s, t) is the distance between s and t. Our second algorithm, given at most n−2 fault nodes and two non-fault nodes s and t in Gn, finds a fault-free path s→t of length at most d(Gn)+3 in O(n) time, where [Formula: see text] is the diameter of Gn. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

scholarly journals Deterministic Approaches to Transient Trajectory Generation

2020 ◽  
Author(s):  
Matthew A. Cooper
Keyword(s):  
Linear Time ◽  
Tracking Error ◽  
Trajectory Generation ◽  
Deterministic Approach ◽  
Van Der Pol ◽  
Linear Time Invariant ◽  
Tuning Method ◽  
Exponential Weighting ◽  
Strongly Nonlinear System ◽  
Optimal Linear

This chapter studies a deterministic approach to transient trajectory generation and control as applied to the forced Van der Pol oscillatory system. This type of system tends towards a strongly nonlinear system, which can be considered chaotic. A classical tuning method, targeted exponential weighting, and isolated trajectory fractionalization trajectory generation methods are examined. Illustrating the given deterministic approach via the Van der Pol system highlights the potentially iterative nature of deterministic methods, and that traditional optimal linear time-invariant control techniques are unable to perform as desired whereas even an idealized nonlinear feedforward control significantly outperforms at the steady-state. It will be shown that utilizing a-priori knowledge of the system dynamics will enable the isolated trajectory fractionalization method to minimize the nonlinear transient effects due to miss-modeled or unmodeled plant dynamics, and that this benefit can be coupled with the targeted exponential weighting approach for greatly decreased trajectory tracking error on the order of a 92% reduction of the objective cost function in the presented case study based on the forced Van der Pol system.

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