Simulated annealing in convex bodies and an O*(n4) volume algorithm

被引：122
|
作者：
Lovász, L
Vempala, S
机构：
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Microsoft Res, Redmond, WA 98052 USA
来源：
JOURNAL OF COMPUTER AND SYSTEM SCIENCES | 2006年 / 72卷 / 02期
基金：
美国国家科学基金会;
关键词：
convex bodies; volume computation; random walks; simulated annealing; logconcave functions;
D O I：
10.1016/j.jcss.2005.08.004
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
We present a new algorithm for computing the volume of a convex body in R-n. The main ingredients of the algorithm are (i) a "morphing" technique that can be viewed as a variant of simulated annealing and (ii) a new rounding algorithm to put a convex body in near-isotropic position. The complexity is O*(n(4)), improving on the previous best algorithm by a factor of n. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：392 / 417
页数：26
相关论文
共 50 条
  • [1] Simulated annealing in convex bodies and an O* (n4) volume algorithm
    Lovász, L
    Vempala, S
    44TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS, 2003, : 650 - 659
  • [2] Computational results of an O*(n4) volume algorithm
    Lovasz, L.
    Deak, I.
    EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2012, 216 (01) : 152 - 161
  • [3] Random walks and an O*(n(5)) volume algorithm for convex bodies
    Kannan, R
    Lovasz, L
    Simonovits, M
    RANDOM STRUCTURES & ALGORITHMS, 1997, 11 (01) : 1 - 50
  • [4] An O(n4) Algorithm for the QAP Linearization Problem
    Kabadi, Santosh N.
    Punnen, Abraham P.
    MATHEMATICS OF OPERATIONS RESEARCH, 2011, 36 (04) : 754 - 761
  • [5] Convex Minimization with Integer Minima in (O)over-tilde (n4) Time
    Jiang, Haotian
    Lee, Yin Tat
    Song, Zhao
    Zhang, Lichen
    PROCEEDINGS OF THE 2024 ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SODA, 2024, : 3659 - 3684
  • [6] Convex Minimization with Integer Minima in Oe(n4) Time
    Jiang, Haotian
    Lee, Yin Tat
    Song, Zhao
    Zhang, Lichen
    arXiv, 2023,
  • [7] SYNTHESIS OF O2'-METHYLURIDINE, O2'-METHYLCYTIDINE, N4,O2'-DIMETHYLCYTIDINE AND N4,N4,O2'-TRIMETHYLCYTIDINE FROM A COMMON INTERMEDIATE
    NYILAS, A
    CHATTOPADHYAYA, J
    ACTA CHEMICA SCANDINAVICA SERIES B-ORGANIC CHEMISTRY AND BIOCHEMISTRY, 1986, 40 (10): : 826 - 830
  • [8] Practical Volume Estimation of Zonotopes by a New Annealing Schedule for Cooling Convex Bodies
    Chalkis, Apostolos
    Emiris, Ioannis Z.
    Fisikopoulos, Vissarion
    MATHEMATICAL SOFTWARE - ICMS 2020, 2020, 12097 : 212 - 221
  • [9] An O(n4) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs
    Feldmann, Andreas Emil
    Widmayer, Peter
    ALGORITHMICA, 2015, 71 (01) : 181 - 200
  • [10] An O(n4) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs
    Feldmann, Andreas Emil
    Widmayer, Peter
    ALGORITHMS - ESA 2011, 2011, 6942 : 143 - 154
12345