TY - JOUR
T1 - Computing a most probable delay constrained path
T2 - NP-hardness and approximation schemes
AU - Xiao, Ying
AU - Thulasiraman, Krishnaiya
AU - Fang, Xi
AU - Yang, Dejun
AU - Xue, Guoliang
N1 - Funding Information:
This research was supported in part by ARO grant W911NF-09-1-0467 and US National Science Foundation (NSF) grant CCF-0830739. The information reported here does not reflect the position or the policy of the federal government. All correspondences should be addressed to Guoliang Xue.
PY - 2012
Y1 - 2012
N2 - 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-\epsilon ) 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.
AB - 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-\epsilon ) 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.
KW - Delay constrained path selection
KW - approximation schemes
KW - computational complexity
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U2 - 10.1109/TC.2011.61
DO - 10.1109/TC.2011.61
M3 - Article
AN - SCOPUS:84859713332
SN - 0018-9340
VL - 61
SP - 738
EP - 744
JO - IEEE Transactions on Computers
JF - IEEE Transactions on Computers
IS - 5
M1 - 5740849
ER -