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In addition, it is optimal in the sense that exactly n steps are required to complete a broadcast in an n-dimensional injured hypercube with up to n -2 faulty links. ... We .also show that n -2 is the maximum number of faulty links that can be tolerated in any optimal broadcast scheme in an n-dimensional hypercube. ... Acknowledgements Thanks to Tianan Wu for providing help in obtaining simulation results. ...doi:10.1016/s1383-7621(96)00023-9 fatcat:vtlhjidqkjc67pnghgj2uh54wi
We consider a broadcasting problem in the n-dimensional hypercube in the shouting communication mode, i.e. any node of a network can inform all its neighbours in one time step. ... In addition, during any time step a number of links of the network can be faulty. Moreover, the faults are dynamic. ... We study this problem for the n-dimensional hypercube network. Given a number m 6 n − 1, the problem is to determine the minimum broadcasting time if at most m faults are allowed in any time step. ...doi:10.1016/s0166-218x(03)00258-0 fatcat:s53tx23255cmbg6k2foy7xjkqq
This paper presents an optimal broadcast algorithm for the hypercube networks. The main focus of the paper is the effectiveness of the algorithm in the presence of many node faults. ... Fu's approach cannot tolerate n − 1 faulty nodes in the worst case, but our approach can tolerate n − 1 faulty nodes. ... Algorithm 1: Broadcasting procedure Input: an n-dimensional hypercube H n with faulty processes and at least one non-faulty process p i in H n Output: the broadcast paths from p i in H n of non-faulty ...doi:10.5281/zenodo.1105517 fatcat:rn6njqdtvvfcfn4a3ga2z3ltfa
This paper presents a method to cope with reliable broadcasting in faulty hypercubes using local safety information. ... The sufficient condition for optimal broadcast of a message is presented in an unsafe hypercube. Extensive simulation results show that the proposed method outperforms previous methods, in all cases. ... Consider the broadcast problem with the source 1010 in the faulty hypercube in Fig. 2 . ...doi:10.1109/tr.2003.810071 fatcat:cizma5iewresjnx5bgk3o6xiau
From Menger’s theorem, it is known that these two problems in H,, can tolerate at most n —k arbitrary faulty nodes. ... Summary: “Embedding meshes in hypercubes has been studied extensively. Most earlier works on embedding in faulty hypercubes considered edge failures as node failures. ...
One application of this construction is a technique to perform broadcasting in a hypercube with faulty links. ... (ii) Every tree in D, is of depth n, which is the optimal depth. (iii) Every edge in the n-cube is shared by at most two trees in D,. ... Various schemes were suggested to deal with the problem of routing and broadcasting in a faulty hypercube [l-4,7,8,10,11] . ...doi:10.1016/0166-218x(94)90175-9 fatcat:qltrvhpatrh7xcdxvap3ksgyfe
For a locally subcube-connected hypercube network that may contain up to 37.5 percent faulty nodes, our algorithms run in linear time and, for any two given nonfaulty nodes, find a routing path of length ... Summary: “We study hypercube networks with a very large num- ber of faulty nodes. ...
Optimal systolic gossip algorithms for complete k-ary trees, in both one-way and two-way communication modes, are described. Finally, in the conclusion, the authors point out two unsolved problems. ... Summary: “We consider scheduling problems in a multiprocessor system with incompatible jobs (two incompatible jobs cannot be processed by the same machine). ...
Parallel Computing on Distributed Memory Multiprocessors
Augmented hypercubes and spare allocation schemes are described. Embedding problems are concerned with finding mappings between two graphs that preserve certain topological properties. ... This paper describes different schemes for tolerating faults in hypercube multiprocessors. ... In  Broadcasting in faulty hypercubes using a d-bit control word was considered in  , where an unsafe node is defined as one that has at least two faulty or unsafe neighbors. ...doi:10.1007/978-3-642-58066-6_14 fatcat:3dbkhliutzeofgfnwzfqz7v2wy
l'his paper performs a detailed evaluation of a faulttolerant distributed broadcasting algorithm for cube connected networks. ... The main areas of evaluation are the following: (1) Algorithm effectiveness in the presence of multiple faults, (2) Establishing the maximum number of link faults allowed, before the algorithm fails to ... For example, in the case of a 3-dimensirmal hypercube with number of faults equal to two, the main module will generate two links faults at random. ...doi:10.1145/131214.131272 dblp:conf/acm/KrullWM92 fatcat:qf3mu5iycjfpvelbc55vqwj6cy
Reliable communication in injured hypercubes with faulty links/nodes using directed safety levels is studied in this paper. ... An injured h y p ercube is a connected hypercube with faulty nodes and/or links. ... Introduction In an injured hypercube, we assume that faulty nodes/links occur (recover) dynamically. ...doi:10.1016/s0743-7315(03)00065-0 fatcat:6lmfinns5vd7zfzpnio4dl7puq
We propose a novel solution in which the reliable broadcasts from individual nodes are interleaved in such a manner that no two packets contend for the same link at any given time-this type of method is ... All-to-all (ATA) reliable broadcast is the problem of reliably distributing information from every node to every other node in point-to-point interconnection networks. ... Dolter, and other members of the Real-Time Computing Laboratory for helpful discussions on the ideas presented in this paper. ...doi:10.1109/71.282556 fatcat:myx5guwo3zesvph2yocj4cbzli
For the hypercube and the complete graph, broadcasting in the linearly bounded fault model can be performed in time logarithmic in the number of nodes. 0 1998 Elsevier Science B.V. ... Every informed node can transmit information to at most one neighbor in a unit of time. Faulty transmissions have no effect. ... In Section 5 we investigate z-safe broadcasting time for hypercubes and complete graphs. Section 6 contains conclusions and open problems. ...doi:10.1016/s0166-218x(97)00107-8 fatcat:7zyxtfcogfc4fad67zy3ixv7g4
Reliable broadcast is a fundamental building block in fault-tolerant distributed systems. ... In this work, we propose a reliable broadcast solution on top of VCube, assuming that the system is asynchronous. ... Formally, reliable broadcast is defined in terms of two primitives: BROADCAST(m), which is defined by the broadcast algorithm and called by the application to disseminate m to all processes, and DELIVER ...doi:10.1186/s13173-017-0064-9 fatcat:qr3rvlickbh4npyf6fcggozx4u
In this paper, we present a new dynamic load-balancing method for hypercube multicomputers with faulty nodes. ... This paper presents a new dynamic load-balancing algorithm for hypercube multicomputers with faulty nodes. ... The gathering of global load information becomes a problem because n stages of information exchange in each of the n dimensions of an n-dimensional faulty hypercube will not be sufficient to gather all ...doi:10.1006/jpdc.1999.1547 fatcat:ojdysniyibeidkz2k6lr4rmjui
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