Abstract

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 .

Highlights

  • Deadlock handling is a very important problem in various applications, including information and database systems, computer networks, massively parallel systems etc

  • In asynchronous distributed systems the problem remains peculiarly subtle and complex. This is because asynchronous system are characterized by the lack of global memory and a common physical clock, as well as by the absence of know bounds on relative processor speeds and message delays

  • Let us analyze an application of KS algorithm for generalized deadlock detection

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Summary

Introduction

Deadlock handling is a very important problem in various applications, including information and database systems, computer networks, massively parallel systems etc. Many of the above mentioned algorithms have been presented, carefully analyzed and compared in two surveys by Knapp ([11]), and Singhal ([16]) These surveys and recent results ([2], [3], [12], [13]) confirm that distributed deadlock detection problem remains difficult, and performance analysis of deadlock handling algorithms still others opportunity for improvement. The latter arises as available performance analysis seems to be incomplete, ambiguous, and of a limited applicability.

Basic Definitions and Problem Formulation
On Time Complexity of BT Algorithm
Complexity Analysis of BT Algorithm
On Time Complexity of KS Algorithm
Initiate a deadlock detection:
Example of KS Algorithm Application
Complexity Analysis of KS Algorithm
Conclusions
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