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14
Faulttolerant message routing in computer networks
 Proc. Int. Conf. on Parallel and Distributed Processing Techniques and Applications
, 1999
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Cycle Breaking in Wormhole Routed Computer Communication Networks
"... Because of its simplicity, low channel setup times, and high performance in delivering messages, wormhole routing has been adopted in second generation multicomputing environments [13]. Furthermore, irregular topologies formed by adhoc interconnection of low cost workstations provide cost effectiv ..."
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Because of its simplicity, low channel setup times, and high performance in delivering messages, wormhole routing has been adopted in second generation multicomputing environments [13]. Furthermore, irregular topologies formed by adhoc interconnection of low cost workstations provide cost effective alternative to massively parallel computing platforms. Switches used in these networks of workstations, NOWs, implement wormhole routing [1, 12]. However, due to a number of channels being held up while requesting others, wormhole routing is susceptible to deadlocks. In this paper we investigated deadlockfree routing algorithms in wormhole routed irregular network topologies. We used a modified version of the Turn Prohibition algorithm [4] to break cycles and prevent channel deadlocks. We then used shortest path algorithm to determine the routing tables for each computational node in the topology, avoiding prohibited turns along the paths from source to destination. We used EMA to import topologies into Opnet and simulated for message delivery using both our approaches and for the competing Up/Down [1] approach. We then repeated this sequence for hundreds of different topologies and determine the average latencies for all algorithms. Our results show that the modified turn prohibition based routing has outperformed both, the original Turn Prohibition and the Up/Down algorithms.
Minimal sets of turns for breaking cycles in graphs modeling networks
 IEEE Trans. Parallel and Distributed Systems
, 2010
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A new algorithm for finding minimal cyclebreaking sets of turns in a graph
 Journal of Graph Algorithms and Applications
, 2006
"... We consider the problem of constructing a minimal cyclebreaking set of turns for a given undirected graph. This problem is important for deadlockfree wormhole routing in computer and communication networks, such as Networks of Workstations. The proposed Cycle Breaking algorithm, or CB algorithm, g ..."
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We consider the problem of constructing a minimal cyclebreaking set of turns for a given undirected graph. This problem is important for deadlockfree wormhole routing in computer and communication networks, such as Networks of Workstations. The proposed Cycle Breaking algorithm, or CB algorithm, guarantees that the constructed set of prohibited turns is minimal and that the fraction of the prohibited turns does not exceed 1/3 for any graph. The computational complexity of the proposed algorithm is O(N 2 ∆), where N is the number of vertices, and ∆ is the maximum node degree. The memory complexity of the algorithm is O(N∆). We provide lower bounds on the minimum size of cyclebreaking sets for connected graphs. Further, we construct minimal cyclebreaking sets and establish bounds on the minimum fraction of prohibited turns for two important classes of graphs, namely, tpartite graphs and graphs with small degrees. The upper bounds are tight and demonstrate the optimality of the CB algorithm for certain classes of graphs. Results of computer simulations illustrate the superiority of the proposed CB algorithm as compared to the wellknown and the widely used Up/Down technique.
Cycles Identifying Vertices and Edges in Binary Hypercubes and 2dimensional Tori
"... A set of subgraphs C1 , C2 , . . . , Ck in a graph G is said to identify the vertices (resp. the edges) if the sets fj : v 2 C j g (resp. fj : e 2 C j g) are nonempty for all the vertices v (edges e) and no two are the same set. We consider the problem of minimizing k when the subgraphs C i are ..."
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A set of subgraphs C1 , C2 , . . . , Ck in a graph G is said to identify the vertices (resp. the edges) if the sets fj : v 2 C j g (resp. fj : e 2 C j g) are nonempty for all the vertices v (edges e) and no two are the same set. We consider the problem of minimizing k when the subgraphs C i are required to be cycles or closed walks. The motivation comes from maintaining multiprocessor systems, and we study the cases when G is the binary hypercube, or the twodimensional pary space endowed with the Lee metric.
A NONADAPTIVE DISTRIBUTED SYSTEMLEVEL DIAGNOSIS METHOD FOR COMPUTER NETWORKS
"... A hierarchical nonadaptive diagnosis algorithm is presented for testing total N nodes of computer networks. Since general computer networks can be regarded as an Nnodes complete graph, then for the efficient testing, it is essential that the test process be parallelized to enable simultaneous test ..."
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A hierarchical nonadaptive diagnosis algorithm is presented for testing total N nodes of computer networks. Since general computer networks can be regarded as an Nnodes complete graph, then for the efficient testing, it is essential that the test process be parallelized to enable simultaneous test of multiple nodes. In order to attain this object, we propose a noble test graph enabling to test as many nodes as possible in a network due to a hierarchical architecture of test processes. The amount of test times is evaluated as the diagnosis latency. Optimal diagnosability t is analyzed under clustered fault distribution. In order to reduce the amount of required test times, two revised approaches are discussed and evaluated.
On the Identification of Vertices Using Cycles
, 2003
"... A set of cycles C 1 ; : : : ; C k in a graph G is said to identify the vertices v if the sets fj : v 2 C j g are all nonempty and dierent. In this paper, bounds for the minimum possible k are given when G is the graph Z p endowed with the Lee or Hamming metric or G is a complete bipartite graph. ..."
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A set of cycles C 1 ; : : : ; C k in a graph G is said to identify the vertices v if the sets fj : v 2 C j g are all nonempty and dierent. In this paper, bounds for the minimum possible k are given when G is the graph Z p endowed with the Lee or Hamming metric or G is a complete bipartite graph.
Improved Bounds for Online MultiPath Routing in Faulty Mesh Networks
, 2006
"... We consider the problem of route discovery in a mesh network with faulty nodes. The number and the positions of the faulty nodes are unknown. It is known that a flooding strategy like expanding ring search can route a message linear in the minimum number of steps d while it causes a traffic (i.e. th ..."
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We consider the problem of route discovery in a mesh network with faulty nodes. The number and the positions of the faulty nodes are unknown. It is known that a flooding strategy like expanding ring search can route a message linear in the minimum number of steps d while it causes a traffic (i.e. the total number of messages) of O(d²). For optimizing traffic a singlepath strategy is optimal producing traffic O(d + p), where p is the number of nodes that are adjacent to faulty nodes. In TRRSFB05077 "Online MultiPath Routing in a Maze" we presented a deterministic multipath online routing algorithm that delivers a message within O(d) steps causing traffic O((d + p) log³ d). Here, we show an improvement of the traffic bound to O((d + p) log² d). This algorithm is asymptotically as fast as flooding and nearly trafficoptimal up to a polylogarithmic factor.
Static faulttolerant scheduling with \pseudotopological " orderings
"... Abstract. We give a graphtheoretical model for oline faulttolerant scheduling of data
ow algorithms onto multiprocessor architectures with distributed memory. Our framework allows the modeling of both processor and channel failures of the \fail silent " type (either transient or permanent) ..."
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Abstract. We give a graphtheoretical model for oline faulttolerant scheduling of data
ow algorithms onto multiprocessor architectures with distributed memory. Our framework allows the modeling of both processor and channel failures of the \fail silent " type (either transient or permanent), and failure masking is achieved by replicating operations and data communications. We show that, in general, the graph representing a faulttolerant scheduling may have circuits; hence, the classical computation of starting/ending times, based upon a topological ordering, is inapplicable. We then provide a notion of \pseudotopological ordering " that permits the computation of the starting/ending times even in the case of cyclic graphs. We also derive algorithms for computing the timeouts that are used for failure detection. 1
UNICAST MESSAGE ROUTING IN СOMMUNICATION NETWORKS WITH IRREGULAR TOPOLOGY
"... Abstract. In this paper we consider the problem of deadlockfree unicast wormhole routing in computer and communication networks with irregular topologies. An example of such networks are Network of Workstations (NOWs). In general, the topology of these networks can be quite random. Several methods ..."
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Abstract. In this paper we consider the problem of deadlockfree unicast wormhole routing in computer and communication networks with irregular topologies. An example of such networks are Network of Workstations (NOWs). In general, the topology of these networks can be quite random. Several methods exist in the literature for wormhole routing in networks/multiprocessors with a regular topology, such as a ndimensional mesh, but very few papers have been published on wormhole routing for irregular networks. Some of these existing techniques require complex signaling hardware at the routers or result in a large amount of congestion at some specific links. The problem of deadlockfree routing consists of two parts. First, all deadlocks must be eliminated. An usual way of doing this, both for regular and irregular topologies, is to forbid some turns. The second part, which is the focus of this paper, is the problem of selecting an optimal (usually the shortest) path after the restrictions on routing have been formulated. We propose three efficient approaches for solving this problem. These approaches (local, global and mixed) differ in a way distances in the network graph are estimated using local information stored in the routers. Our approach for nonadaptive unicast deadlockfree wormhole routing provides for message paths very close to the shortest ones and more uniform distribution of the traffic between communication links in the system. Initial simulation results presented in the paper indicate that the proposed approaches are promising in terms of both throughput and scalability. Key Words. Wormhole routing, deadlock elimination, multiprocessor systems. 1.