On Time Complexity of Distributed Algorithms for Generalized Deadlock Detection

Deadlock detection in distributed asynchronous systems such as distributed database systems, computer networks, massively parallel systems etc. is peculiarly subtle and complex. This is because asynchronous systems are characterized by the lack of global memory and a common physical clock, as well as by the absence of known bounds on relative processor speeds and transmission delays. These difficulties imply also problems with performance analysis of distributed algorithms for deadlock detection. This paper deals with worst-case one-time complexity analysis of two well known distributed algorithms for generalized deadlock detection. The time complexity is expressed as a function of the diameter d and the longest path l of the wait-for-graph (WFG) characterizing a state of distributed system. First, the algorithm proposed by Bracha and Toueg is considered. It is shown that its time complexity is of 2d+2l. Then, we prove that the time complexity of Kshemkalyani and Singhal algorithm is of (d+ 1) + l.