heap base coordinator finding with fault tolerant … · heap base coordinator finding with fault...

Heap Base Coordinator Finding with Fault Tolerant Method in Distributed Systems

Mehdi EffatParvar 1, AmirMasoud Rahmani2, MohammadReza EffatParvar3, Mehdi Dehghan4 1 ECE Department, Islamic Azad University- Ardabil Branch, Ardabil, Iran

2 ECE Department, Islamic Azad University- Tehran Since and Research Branch, Tehran, Iran 3 ECE Department of Tehran University, Tehran, Iran

4 Computer and IT Eng Department of AmirKabir University of Technology, Tehran, Iran

Abstract Coordinator finding in wireless networks is a very

important problem, and this problem is solved by suitable algorithms. The main goals of coordinator finding are synchronizing the processes at optimal using of the resources. Many different algorithms have been presented for coordinator finding. The most important leader election algorithms are the Bully and Ring algorithms. In this paper we analyze and compare these algorithms with together and we propose new approach with fault tolerant mechanisms base on heap for coordinator finding in wireless environment. Our algorithm's running time and message complexity compare favorably with existing algorithms. Our work involves substantial modifications of an existing algorithm and its proof, and we adapt the existing algorithms to the noisy environment base on fault tolerant mechanisms.

1. Introduction

Election of a leader is a fundamental problem in

distributed computing. It has been the subject of intensive research since its important was first articulated by Gerard Lelann [1]. The practical importance of election in a distributed computing is further emphasized by Garcia Molina’s Bully algorithm [3].

In a pure distributed system, there is no central controlling processor that arbitrates decisions. Without a central authority or coordinator, any processor has to communicate with all processors in the network to make decision. Often during the decision process, not all processors make the same decision. Communication between processors takes time and further more, making the decision takes time. Coordination among processors becomes difficult when consistency is needed among all processors.

Leader election is a technique that can be used to break the symmetry of distributed Systems [5].

Some applications of leader election include finding a spanning tree with the elected leader as root[18], breaking a deadlock , reconstructing a lost token in a token ring network, using leader election in Ad Hoc network [16,17].

Leader election algorithms for static networks have been proposed in [19]. These algorithms work by constructing several spanning trees with a prospective leader at the root of the spanning tree and recursively reducing the number of spanning trees to one. However, these algorithms work only if the topology remains static and hence cannot be used in a mobile setting [8, 9].

Leader election is a useful building block in distributed systems, whether wired or wireless, especially when failures can occur. For example, if a node failure causes the token to be lost in a mutual exclusion algorithm, then the other nodes can elect a new leader to hold a replacement token. Leader election can also be used in group communication protocols, to choose a new coordinator when the group membership changes. The standard definition of the leader election problem for static networks [4] is that:

1. Eventually there is a leader and 2. There should never be more than one leader. In general election algorithm attempt to locate the

process with the highest process number and designate it as coordinator the algorithm differ in the way they do the location. Furthermore we also assume that every process know the process number of every other process. What the processes do not know is which ones are currently up and which ones are currently down. The goal of an election algorithm is to ensure that when an election starts, it concludes whit all processes agreeing on who the new coordinator is to be.

Several leader election algorithms have been

proposed over the years [5-12]. Some of the grand election algorithms that we can mention to them are Bully algorithm, Ring algorithm, Chang and Roberts’ algorithm [13], Peterson’s election algorithm [15], Lelann’s algorithm [1], Franklin’s algorithm [14]. Such leader election algorithms proposed until now require processors to be directly involved in leader election. Information is exchanged between processors by transmitting messages to each other. The processors exchange messages with each other and try to reach an agreement. Once an agreement is reached, a processor will be elected as leader and all other processors will acknowledge the presence of the leader.

The rest of paper organized as follow: in section 2 we describe our modified Bully algorithm, section 3 propose the heap base election, in section 4 we explain the fault tolerant method base on heap tree, section 5 discusses

Mehdi Effat Parvar et al, Int. J. Comp. Tech. Appl., Vol 2 (4), 761-766

IJCTA | JULY-AUGUST 2011 Available [email protected]

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about analytical simulation and section 6 presents the conclusion and future works.

2. Modified Bully Algorithm with Fault

Tolerant Mechanism As it has been mentioned, in Bully algorithm the

number of messages that should be exchanged between processes is very high. In previous section we presented the new approach with sort mechanism and we decreased the number of messages. Bully with the sort mechanism has a little message passing, but it may consume more time in contrast with Bully algorithm to find the leader, we describe another approach to modify Bully. In this algorithm [2] when process P notices that the leader has crashed, it sends an election message to all processes with higher ID number.

Each process that receives election message sends its ID as a respond to process P. If no process responses to process P, it will broadcast one coordinator message to all processes. If some processes response to process P, it will select the process with the highest ID number as coordinator and that will send a new message with

selected ID number to all processes. In this manner all processes know the new leader. This approach is a suitable way to select the leader, but when the process with the highest ID number is sent, its message to process P maybe lost. So we want to present a fault tolerant mechanism to prevent this fault. To do this, when process P selected the highest ID number it sends the selected ID to all processes, now the new leader sends election message to processes with greater ID number to be sure that there is no process with great ID numbers. If a message is received from processes with great ID numbers, it introduces the greatest one as leader. Otherwise it remains the leader again.

In the rest of this paper we compare the number of message passing of these methods with together and also we compare them with Modified Ring algorithm [2].

3. Leader Election with Heap Tree

In this section we will describe other leader election

algorithm. In this method we use the heap tree for selecting the leader. Each node of the tree corresponds to an element of the array that stores the value in the node. The tree is completely filled on all levels except possibly the lowest, which is filled from the left up to a point. An array A that represents a heap is an object with two attributes: length [A], which is the number of elements in the array, and heap-size [A], the number of elements in the heap stored within array A. That is, although A[1 .. length[A]] may contain valid numbers, no element past A[heap-size[A]], where heap-size[A] ≤ length[A], is an element of the heap.

The root of the tree is A[1], and given the index i of a node, the indices of its parent PARENT(i), left child LEFT(i), and right child RIGHT(i) can be computed simply.

On most computers, the LEFT procedure can compute 2i in one instruction by simply shifting the binary representation of i left one bit position. Similarly, the RIGHT procedure can quickly compute 2i +1 by shifting the binary representation of i left one bit position and adding in a 1 as the low-order bit. The PARENT

procedure can compute 2/i by shifting i right one bit

position. There are two kinds of binary heaps: max-heaps and

min-heaps. The values in the nodes satisfy a heap property, the

specifics of which depend on the kind of heap. In a max-heap, the max-heap property is that for every node i other than the root, A[PARENT(i)] ≥ A[i ] , that is, the value of a node is at most the value of its parent. Thus, the largest element in a max-heap is stored at the root, and the sub tree rooted at a node contains values no larger than that contained at the node itself. A min-heap is organized in the opposite way; the min-heap property is that for every node i other than the root, A[PARENT(i)] ≤ A[i ] .

The smallest element in a min-heap is at the root. The MAX-HEAPIFY procedure, which runs in O(log n) time, is the key to maintaining the max-heap property.

(e) (f)

Figure 1: Process 2 notices the coordinator has crashed so sends an election message to processes 3,4,5(a), and receives OK message from processes 3,4 it means that Ok message of process 5 is failed (b), then process 4 is selected as a coordinator (c), and process 4 according to algorithm sends an election message and selects process 5 as a coordinator (d,e,f)

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7. References [1] G. LeLann. “Distributed systems - towards a formal approach”, Information Processing Letters, 1977, pp. 155-160. [2] M. EffatParvar, M.R. EffatParvar, A. Bemana, M. Dehghan, “Determining a Central Controlling Processor with Fault Tolerant Method in Distributed System,” In Proc. of ITNG07, IEEE, May 2007. [3] H.Garcia-Molina. “Electronic in Distributed Computing System”. IEEE Transaction Computers, |Vol.C-31,pp. 48-59, Jan. 1982. [4] H. Attiya and J. L. Welch. Distributed Computing: Fundamentals, Simulations and Advanced Topics. London, UK: McGraw-Hill, 1998. [5] G. Fredrickson and N. Lynch, “The impact of synchronous communication on the problem of electing a leader in a ring,” in Proc. 16th Annu. ACM Symp. on Theory of Computing, Washington, D.C., 1984, pp. 493-503. [6] E. Gafni and Y. Afek, “Election and traversal in unidirectional networks,” in Proc. 3rd Annu. ACM Symp. on Principles of Distributed Computing, Vancouver, B.C., Canada, Aug. 1984, pp. 190-198. [7] R. G. Gallager, Choosing a leader in a network, Unpublished memorandum, M.I.T., Cambridge, Mass., 1977. [8] R. G. Gallager, P. M. Humblet, and P. M. Spira, “A distributed algorithm for minimum-weight spanning trees,” ACM Trans. Program. Lang. Syst., vol. 5, no. 1, pp. 66-77, Jan. 1983. [9] P. Humblet, “Selecting a leader in a clique in O(n log n) messages,” in Intern. Memo., Laboratory for Information and Decision Systems, M.I.T., Cambridge, Mass., 1984. [10] E. Korach, S. Moran, and S. Zaks, “Tight lower and upper bounds for some distributed algorithms for a complete network of processors,” in Proc. 3rd Annu. ACM Symp. on Principles of Distributed Computing, Vancouver, B.C., Canada, pp. 199-207, Aug. 1984. [11] I. Lavalléé and G. Roucairol, “A fully distributed (minimal) spanning tree algorithm,” Information Processing Letters, 23, pp. 55-62, Aug. 1986. [12] P. M. B. Vitanyi, “Distributed election in an Archimedean ring of processors,” in Proc. 16th Annu. ACM Symp. on Theory of Computing, Washington, D.C., pp. 542-547, 1984. [13] E. Chang and R. Roberts, “An improved algorithm for decentralized extrema-finding in circular configurations of processes,” Communications of the ACM}, pp. 281-283, 22, 5, 1979. [14] W. R. Franklin, “On an improved algorithm for decentralized extrema finding in circular configurations of processors,” Communication of the ACM, pp. 336-337, 25, 1982. [15] G. L. Peterson, “An O(nlogn) unidirectional algorithm for the circular extrema problem,” ACM Trans. Program. Lang. Syst. 758-762, 4,4 (Oct. 1982). [16] N. Malpani, J. Welch and N. Vaidya, “Leader Election Algorithms for Mobile Ad Hoc Networks,” In Fourth International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, Boston, MA, August 2000. [17] P. Basu, N. Khan and T. Little, “A Mobility based metric for clustering in mobile ad hoc networks,” In International Workshop on Wireless Networks and Mobile Computing, Apr. 2001. [18] R. Gallager, P. Humblet and P. Spira, “A Distributed Algorithm for MinimumWeight Spanning Trees,” In ACM Transactions on Programming Languages and Systems, vol.4, no.1, pages 66-77, January 1983. [19] D. Peleg, “Time Optimal Leader Election in General Networks,” In Journal of Parallel and Distributed Computing, vol.8, no.1, pages 96-99, January 1990.



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