Adaptive Fault-Tolerant Routing in 2D Mesh with Cracky Rectangular Model

Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2014, Article ID 592638, 10 pages http://dx.doi.org/10.1155/2014/592638 Research Article Adaptive Fault-Tolerant Routing in 2D Mesh with Cracky Rectangular Model Yi Yang,1 Meirun Chen,2 Hao Li,3 and Lian Li1 1 School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China 3 Laboratoire de Recherche en Informatique, Bat 490, Universite Paris-Sud 11, 91405 Orsay Cedex, France 2 Correspondence should be addressed to Yi Yang; Received 7 February 2014; Accepted 9 March 2014; Published 7 April 2014 Academic Editor: X. Song Copyright © 2014 Yi Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper mainly focuses on routing in two-dimensional mesh networks. We propose a novel faulty block model, which is cracky rectangular block, for fault-tolerant adaptive routing. All the faulty nodes and faulty links are surrounded in this type of block, which is a convex structure, in order to avoid routing livelock. Additionally, the model constructs the interior spanning forest for each block in order to keep in touch with the nodes inside of each block. The procedure for block construction is dynamically and totally distributed. The construction algorithm is simple and ease of implementation. And this is a fully adaptive block which will dynamically adjust its scale in accordance with the situation of networks, either the fault emergence or the fault recovery, without shutdown of the system. Based on this model, we also develop a distributed fault-tolerant routing algorithm. Then we give the formal proof for this algorithm to guarantee that messages will always reach their destinations if and only if the destination nodes keep connecting with these mesh networks. So the new model and routing algorithm maximize the availability of the nodes in networks. This is a noticeable overall improvement of fault tolerability of the system. 1. Introduction In the last decades, the goal of many researchers was to study communication operations in networks with fixed topologies, including modeling architectures and routing algorithm of parallel computers and cluster or middle area communication networks (such as metropolitan networks covering a town or a small region). The quality of such networks strongly depends on correct and efficient execution of communication operations. Direct networks [1] become a popular architecture for communication networks, especially in massively parallel computer system. In direct networks, nodes (computers) are connected to only a few nodes, that is, its neighbours, according to the topology of the networks and communicate with each other by exchanging messages. Moreover, the mesh structure is one of the most important topology of direct networks. Especially, low dimensional mesh networks, due to its low node degree, are more popular than the high dimensional mesh networks. Currently most of architecture of parallel computers is based on two-dimensional mesh topology, for example, Seitz et al. 1988 [2], Intel Touchstone DELTA [3, 4], and Intel paragon. Several models based on direct networks have been studied ([5–9]), especially the two-dimensional mesh ([10– 16], etc.) for communication operations. The purposes of these papers mainly focus on how to route messages in the two-dimensional mesh. Routing is the process to send messages from source nodes to destination nodes, passing some intermediate nodes. A very important aspect of message routing is its ability to route from a source node to a destination node, avoiding all faulty nodes or links. Basically, there are two types of message routing: (1) deterministic routing that is routing in which the routes between given pairs of nodes are determined in advance of transmission, (2) adaptive routing that allows us to take any path between its source and its final destination; that is, 2 Journal of Applied Mathematics the path is adaptively constructed in the process of routing. The deterministic routing algorithms are simple and ease of implementation, this is the advantage for deterministic routing. However, adaptive routing can reduce network latency and increase network throughput and the most attractive point is that it can tolerant more faults than deterministic routing [17]. Thus the latter one emerged as an attractive field. In most papers on this field, they often considered how to make a path between source and destination node pairs, avoiding the faulty nodes, and most work used the disconnected rectangular block fault model [11]. The disconnected rectangular blocks are composed of the faulty nodes and their neighboring nonfaulty nodes with the principle of maintaining rectangular shape. As a result, adaptive routing can tolerate faulty nodes by bypassing these rectangles. However, in order to maintain its rectangular shape, the block has to group some nonfaulty nodes inside, called unsafe nodes in these papers. Of course, these unsafe nodes will never be used until their corresponding blocks recovery, and the messages will never be sent to these nodes, while they should be (as illustrated in Figure 1). Chien and Kim [18] present a partially adaptive algorithm for mesh networks. The basic idea is to use the algorithm to circumfuse any convex faulty regions. If faulty regions are not naturally convex, good nodes and links are marked as faulty until the regions become convex. However, once the faults are located on a boundary, in order to tolerate faults, all nodes form that boundary will become faulty. Boppana and Chalasani [10] use 𝑓-chain and 𝑓-ring, which is an extension of disconnected rectangular block fault model, to route the messages around them, and 𝑓-chain addresses the boundary problem in the Chien and Kim’s paper. But the 𝑓chain and 𝑓-ring may connect with each other; this makes the routing algorithm more complex than [18]. In [11], Su and Shin assume a node to be the basic fault element. They construct the blocks based only on the faulty nodes; thus they can only tolerate faulty nodes except the faulty links. Overall, the construction of these faulty regions is static; that is, once these regions are constructed, all nodes including the good ones in these regions cannot join in routing any more. The faulty regions are not self-adaptive; that is, if some of faulty nodes in these faulty regions are fixed well, then the faulty regions will be held as they were, but actually they can release some good nodes and become smaller ones keeping convex shape. Adaptive fault-tolerance routing technologies are also using in WSN (Wireless Sensor Networks), MEMS (MicroElectro-Mechanical Systems) and SoC (System on Chip) to increase the usability (...truncated)