A TIGHT LOWER BOUND FOR THE TRAIN REVERSAL PROBLEM

被引:0
|
作者
AGGARWAL, A
LEIGHTON, T
机构
[1] MIT,MATH,CAMBRIDGE,MA 02139
[2] MIT,COMP SCI LAB,CAMBRIDGE,MA 02139
关键词
Lower bound; one-car spur; recursive algorithm; reversing a train; upper bound;
D O I
10.1016/0020-0190(90)90032-S
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In a 1987 Scientific American Computer Recreations article, A.K. Dewdney posed the problem of reversing an n-car train on a track with a one-car spur using the minimum amount of work. In that article, Dewdney indicated an algorithm for reversing the train that uses O(n3) work. Shortly thereafter, Amato, Blum, Irani and Rubinfeld (Reversing Trains: A Turn of the Century Sorting Problem, J. Algorithms, Vol. 10, 1989, pp. 413-428) discovered a simple recursive algorithm that requires O(n2logn) work to reverse a train. In this paper, we prove that Amato et al.'s algorithm is optimal up to a constant factor, i.e., we prove that any algorithm for reversing an n-car train in the Dewdney model requires Ω(n2log n) work. © 1990.
引用
收藏
页码:301 / 304
页数:4
相关论文
共 50 条
  • [1] Tight Lower Bound for the Channel Assignment Problem
    Socala, Arkadiusz
    [J]. ACM TRANSACTIONS ON ALGORITHMS, 2016, 12 (04)
  • [2] A tight lower bound for the completion time variance problem
    Ng, CT
    Cai, X
    Cheng, TCE
    [J]. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1996, 92 (01) : 211 - 213
  • [3] A tight lower bound for the Steiner Point Removal problem on trees
    Chan, T. -H. Hubert
    Xia, Donglin
    Konjevod, Goran
    Richa, Andrea
    [J]. APPROXIMATION, RANDOMIZATION AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES, 2006, 4110 : 70 - 81
  • [4] A TIGHT AMORTIZED BOUND FOR PATH REVERSAL
    GINAT, D
    SLEATOR, DD
    TARJAN, RE
    [J]. INFORMATION PROCESSING LETTERS, 1989, 31 (01) : 3 - 5
  • [5] A NEW LOWER-BOUND TECHNIQUE AND ITS APPLICATION - TIGHT LOWER-BOUND FOR A POLYGON TRIANGULATION PROBLEM
    RAMANAN, P
    [J]. SIAM JOURNAL ON COMPUTING, 1994, 23 (04) : 834 - 851
  • [6] A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem
    Barak, Boaz
    Hopkins, Samuel B.
    Kelner, Jonathan
    Kothari, Pravesh
    Moitra, Ankur
    Potechin, Aaron
    [J]. 2016 IEEE 57TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS), 2016, : 428 - 437
  • [7] A computational study of the permutation flow shop problem based on a tight lower bound
    Ladhari, T
    Haouari, M
    [J]. COMPUTERS & OPERATIONS RESEARCH, 2005, 32 (07) : 1831 - 1847
  • [8] A tight lower bound for the online bounded space hypercube bin packing problem
    Kohayakawa, Yoshiharu
    Miyazawa, Flavio Keidi
    Wakabayashi, Yoshiko
    [J]. DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2021, 23 (03):
  • [9] A NEARLY TIGHT SUM-OF-SQUARES LOWER BOUND FOR THE PLANTED CLIQUE PROBLEM
    Barak, Boaz
    Hopkins, Samuel
    Kelner, Jonathan
    Kothari, Pravesh K.
    Moitra, Ankur
    Potechin, Aaron
    [J]. SIAM JOURNAL ON COMPUTING, 2019, 48 (02) : 687 - 735
  • [10] A Near-Tight Approximation Lower Bound and Algorithm for the Kidnapped Robot Problem
    Koenig, Sven
    Mudgal, Apurva
    Tovey, Craig
    [J]. PROCEEDINGS OF THE SEVENTHEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2006, : 133 - +