Issue No. 05 - May (2012 vol. 61)
ISSN: 0018-9340
pp: 738-744
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
ABSTRACT
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.
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. , pp. 738-744, May 2012, doi:10.1109/TC.2011.61