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Computing a Most Probable Delay Constrained Path: NP-Hardness and Approximation Schemes
May 2012 (vol. 61 no. 5)
pp. 738-744
ASCII Text
x 
 
Guoliang Xue, Dejun Yang, Xi Fang, K. Thulasiraman, Ying Xiao, "Computing a Most Probable Delay Constrained Path: NP-Hardness and Approximation Schemes," IEEE Transactions on Computers, vol. 61, no. 5, pp. 738-744, May, 2012.
 
 
BibTex
x
 
@article{ 10.1109/TC.2011.61,
author = { Guoliang Xue and Dejun Yang and Xi Fang and K. Thulasiraman and Ying Xiao},
title = {Computing a Most Probable Delay Constrained Path: NP-Hardness and Approximation Schemes},
journal ={IEEE Transactions on Computers},
volume = {61},
number = {5},
issn = {0018-9340},
year = {2012},
pages = {738-744},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2011.61},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Computing a Most Probable Delay Constrained Path: NP-Hardness and Approximation Schemes
IS - 5
SN - 0018-9340
SP738
EP744
EPD - 738-744
A1 - Guoliang Xue,
A1 - Dejun Yang,
A1 - Xi Fang,
A1 - K. Thulasiraman,
A1 - Ying Xiao,
PY - 2012
KW - probability
KW - approximation theory
KW - computational complexity
KW - directed graphs
KW - time complexity
KW - NP-Hardness
KW - approximation schemes
KW - delay constrained path selection
KW - source-to-destination path
KW - delay bound
KW - directed graph
KW - known mean
KW - known variance
KW - fully polynomial time approximation scheme
KW - probability
KW - Delay
KW - Approximation methods
KW - Polynomials
KW - Approximation algorithms
KW - Algorithm design and analysis
KW - Upper bound
KW - Routing
KW - approximation schemes.
KW - Delay constrained path selection
KW - computational complexity
VL - 61
JA - IEEE Transactions on Computers
ER -
 
Guoliang Xue, Sch. of Comput., Inf. & Decision Syst. Eng., Arizona State Univ., Tempe, AZ, USA
Dejun Yang, Sch. of Comput., Inf. & Decision Syst. Eng., Arizona State Univ., Tempe, AZ, USA
Xi Fang, Sch. of Comput., Inf. & Decision Syst. Eng., Arizona State Univ., Tempe, AZ, USA
K. Thulasiraman, Sch. of Comput. Sci., Univ. of Oklahoma, Norman, OK, USA
Ying Xiao, Sch. of Comput. Sci., Univ. of Oklahoma, Norman, OK, USA
Delay constrained path selection is concerned with finding a source-to-destination path so that the delay of the path is within a given delay bound. When the network is modeled by a directed graph where the delay of a link is a random variable with a known mean and a known variance, the problem becomes that of computing a most probable delay constrained path. In this paper, we present a comprehensive theoretical study of this problem. First, we prove that the problem is NP-hard. Next, for the case where there exists a source-to-destination path with a delay mean no more than the given delay bound, we present a fully polynomial time approximation scheme. In other words, for any given constant ε such that 0 <; ε <; 1, our algorithm computes a path whose probability of satisfying the delay constraint is at least (1-ε) times the probability that the optimal path satisfies the delay constraint, with a time complexity bounded by a polynomial in the number of network nodes and 1/ε. Finally, for the case where any source-to-destination path has a delay mean larger than the given delay bound, we present a simple approximation algorithm with an approximation ratio bounded by the square root of the hop count of the optimal path.

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Index Terms:
probability,approximation theory,computational complexity,directed graphs,time complexity,NP-Hardness,approximation schemes,delay constrained path selection,source-to-destination path,delay bound,directed graph,known mean,known variance,fully polynomial time approximation scheme,probability,Delay,Approximation methods,Polynomials,Approximation algorithms,Algorithm design and analysis,Upper bound,Routing,approximation schemes.,Delay constrained path selection,computational complexity
Citation:
Guoliang Xue, Dejun Yang, Xi Fang, K. Thulasiraman, Ying Xiao, "Computing a Most Probable Delay Constrained Path: NP-Hardness and Approximation Schemes," IEEE Transactions on Computers, vol. 61, no. 5, pp. 738-744, May 2012, doi:10.1109/TC.2011.61
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