A POLYNOMIAL TIME ALGORITHM FOR COMPUTING EXTINCTION PROBABILITIES OF MULTITYPE BRANCHING PROCESSES

被引：1

作者：

Etessami, Kousha ^{[1
]}

Stewart, Alistair ^{[2
]}

Yannakakis, Mihalis ^{[3
]}

机构：

[1] Univ Edinburgh, Sch Informat, Edinburgh EH8 9AB, Midlothian, Scotland

[2] Univ Southern Calif, Dept Comp Sci, Los Angeles, CA 90007 USA

[3] Columbia Univ, Dept Comp Sci, New York, NY 10027 USA

来源：

SIAM JOURNAL ON COMPUTING | 2017年 / 46卷 / 05期

关键词：

multitype branching processes; extinction probabilities; polynomial time algorithms; nonlinear systems of equations; Newton's method; computational complexity; COMPLEXITY; TREE;

D O I：

10.1137/16M105678X

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/c), where c > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open problems regarding the computational complexity of computing key quantities associated with some classic and well studied stochastic processes, including multitype branching processes and stochastic context-free grammars.

引用

页码：1515 / 1553

页数：39

共 50 条

[41] EXTINCTION PROBABILITIES FOR AGE-DEPENDENT AND POSITION-DEPENDENT BRANCHING PROCESSES
CONNER, HE
[J]. JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1964, 12 (04): : 899 - 909
[42] Multitype branching processes and some queueing systems
Vatutin V.A.
Dyakonova E.E.
[J]. Journal of Mathematical Sciences, 2002, 111 (6) : 3901 - 3911
[43] Inclusive Fitness from Multitype Branching Processes
Geoff Wild
[J]. Bulletin of Mathematical Biology, 2011, 73 : 1028 - 1051
[44] Multitype branching processes evolving in a Markovian environment
Dyakonova, E. E.
[J]. DISCRETE MATHEMATICS AND APPLICATIONS, 2012, 22 (5-6): : 639 - 664
[45] APPROXIMATION OF AGE DEPENDENT, MULTITYPE BRANCHING PROCESSES
KURTZ, TG
[J]. ANNALS OF MATHEMATICAL STATISTICS, 1970, 41 (02): : 363 - &
[46] ON MULTITYPE BRANCHING-PROCESSES IN A RANDOM ENVIRONMENT
TANNY, D
[J]. ADVANCES IN APPLIED PROBABILITY, 1981, 13 (03) : 464 - 497
[47] MULTITYPE BRANCHING-PROCESSES - ASYMPTOTIC RESULTS
CARVALHO, ML
MULLER, D
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1983, 296 (07): : 337 - 340
[48] Large deviations for supercritical multitype branching processes
Jones, OD
[J]. JOURNAL OF APPLIED PROBABILITY, 2004, 41 (03) : 703 - 720
[49] Multitype subcritical branching processes in a random environment
Dyakonova, E. E.
[J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 282 (01) : 80 - 89
[50] Critical multitype branching processes in a random environment
Dyakonova, E. E.
[J]. DISCRETE MATHEMATICS AND APPLICATIONS, 2007, 17 (06): : 587 - 606

← 1 2 3 4 5 →