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Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 35 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
EdgeDisjoint Spanning Trees on the Star Network with Applications to Fault Tolerance
 IEEE Trans. Computers
, 1996
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The Spanning Diameter of the Star Graphs
"... Assume that u and v are any two distinct vertices of dierent partite sets of the ndimensional star graph Sn with n 5. We prove that there are (n 1) internally disjoint paths P1; P2; : : : ; Pn1 joining u to v such that [ n1 i=1 Pi spans Sn and l(Pi) (n1)!+2(n2)!+2(n3)!+1 = n! n2 +1. We also prov ..."
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Cited by 1 (1 self)
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Assume that u and v are any two distinct vertices of dierent partite sets of the ndimensional star graph Sn with n 5. We prove that there are (n 1) internally disjoint paths P1; P2; : : : ; Pn1 joining u to v such that [ n1 i=1 Pi spans Sn and l(Pi) (n1)!+2(n2)!+2(n3)!+1 = n! n2 +1. We also prove that there are two internally disjoint paths Q1 and Q2 joining u to v such that Q1[Q2 spans Sn and l(Qi) n!
A Routing Algorithm for the Star Interconnection Network in the Presence of Faults
"... This paper presents a fault tolerant routing algorithm for the star graph. The suggested algorithm is based on the concept of unsafety vectors, originally proposed for hypercubes. In this algorithm, each node starts by computing a first level unsafety set, composed of the set of unreachable neighbor ..."
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This paper presents a fault tolerant routing algorithm for the star graph. The suggested algorithm is based on the concept of unsafety vectors, originally proposed for hypercubes. In this algorithm, each node starts by computing a first level unsafety set, composed of the set of unreachable neighbors. It then performs some exchanges with its neighbors to determine the unsafety nodes. After that, all nodes have the addresses of all faulty nodes. Based on the information gathered in each node, faulttolerant routing between a source node and a destination node is realized. We conducted a performance comparison between the star and hypercube graph using the unsafety vectors routing algorithm under different working conditions. The results obtained through simulation experiments reveal that the hypercube is of superior performance compared to the star graph in the presence of low fault rates. But its performance under high fault rates falls short of that of the star graph.
Deterministic Models of Communication Faults?
"... Abstract. In this paper we survey some results concerning the impact of faulty environments on the solvability and complexity of communication tasks. In particular, we focus on deterministic models of faults in synchronous networks, and show how different variations of the model influence the perfo ..."
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Abstract. In this paper we survey some results concerning the impact of faulty environments on the solvability and complexity of communication tasks. In particular, we focus on deterministic models of faults in synchronous networks, and show how different variations of the model influence the performance bounds of broadcasting algorithms. 1
EXTENDED FAULTDIAMETER OF STAR GRAPHS
"... Abstract. An important issue in computer communication networks is faulttolerant routing. A popular graph topology for interconnection network is the star graph [1]. We know from [6] that if up to 2n−4 vertices are deleted, the resulting graph has a single large component and at most one other comp ..."
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Abstract. An important issue in computer communication networks is faulttolerant routing. A popular graph topology for interconnection network is the star graph [1]. We know from [6] that if up to 2n−4 vertices are deleted, the resulting graph has a single large component and at most one other component of size at most two. This paper will discuss routing in the large component and also show that its diameter in the faulty star graph is bounded by diam(Sn) + 9.
Routing Problems in Incomplete Rotator Graphs
"... Abstract A rotator graph was proposed as a topology for interconnection networks of parallel computers, and it has a merit that it can connect many nodes with small diameter and small degree. However, the number of nodes in a rotator graph must be equal to the factorial of an integer, which causes a ..."
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Abstract A rotator graph was proposed as a topology for interconnection networks of parallel computers, and it has a merit that it can connect many nodes with small diameter and small degree. However, the number of nodes in a rotator graph must be equal to the factorial of an integer, which causes a demerit that it lacks incremental expandability. In this paper, we propose a graph, an incomplete rotator graph, that is obtained by deleting some of sub graphs of a rotator graph, and we give algorithms for the problems of the simple routing, the Hamiltonian cycle, and the container.
Reliable Communication in Faulty Star Networks
"... Abstract ‘ We take advantage of the hierarchical structure of the star graph network to obtain an efficient method for constructing nodedisjoint paths between arbitrary pairs of nodes in the network. A distributed faulttolerant routing algorithm for the star network based on this construction metho ..."
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Abstract ‘ We take advantage of the hierarchical structure of the star graph network to obtain an efficient method for constructing nodedisjoint paths between arbitrary pairs of nodes in the network. A distributed faulttolerant routing algorithm for the star network based on this construction method is then presented and evaluated. The proposed algorithm adapts the routing decisions in response to node failures. Node failure and repair conditions may arise dynamically (at any time) provided that the total number of faulty nodes at any given time is less than the nodeconnectivity n1 of the nstar. We show that if the node failures occur ’reasonably … apart in time, then all messages will be routed on paths of length δ + ε where δ is the minimum distance between the source and the destination and ε is 0, 2, or 4. In the unlikely case where more failures occur in a ’short period…, the algorithm still delivers all messages but via possibly longer paths. Index Terms ‘ Fault tolerance, star graph, routing, nodedisjoint paths, distributed algorithm. 1.