Abstract. In this paper we propose and prove that cyclic quorum sets can efficiently manage all-pairs computations and data replication. The quorums are O(N/√P) in size, up to 50% smaller than the dual N/√P array implementations, and significantly smaller than solutions requiring all data. Implementation evaluation demonstrated scalability on real datasets with a 7x speed up on 8 nodes with 1/3 rd the memory usage per process. The all-pairs problem requires all data elements to be paired with all other data elements. These all-pair problems occur in many science fields, which has led to their continued interest. Additionally, as datasets grow in size, new methods like these that can reduce memory footprints and distribute work equally across compute nodes will be demanded.

Many optical networks face heterogeneous communication requests requiring topologies to be efficient and fault tolerant. For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. We show efficiency and distributed control can also be accomplished in optical network routing by applying the same established quorum set theory.Cycle-based optical network routing, whether using SONET rings or p-cycles, provides the sufficient reliability in the network. Light-trails forming a cycle allow broadcasts within a cycle to be used for efficient multicasts. Cyclic quorum sets also have all pairs of nodes occurring in one or more quorums, so efficient, arbitrary unicast communication can occur between any two nodes. Efficient broadcasts to all network nodes are possible by a node broadcasting to all quorum cycles to which it belongs (O( √ N )). In this paper, we propose applying the distributed efficiency of the quorum sets to routing optical cycles based on light-trails. With this new method of topology construction, unicast and multicast communication requests do not need to be known or even modeled a priori. Additionally, in the presence of network link faults, greater than 99% average coverage enables the continued operation of nearly all arbitrary unicast and multicast requests in the network. Finally, to further improve the fault coverage, an augmentation to the ECBRA cycle finding algorithm is proposed.

In this paper we propose a cycle redundancy technique that provides optical networks almost fault-tolerant pointto-point and multipoint-to-multipoint communications. The technique more importantly is shown to approximately halve the necessary light-trail resources in the network while maintaining the fault-tolerance and dependability expected from cycle-based routing.For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Optimal communication quorum sets forming optical cycles based on light-trails have been shown to flexibly and efficiently route both point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle routing techniques will use pairs of cycles to achieve both routing and faulttolerance, which uses substantial resources and creates the potential for underutilization. Instead, we intentionally utilize redundancy within the quorum cycles for fault-tolerance such that almost every point-to-point communication occurs in more than one cycle. The result is a set of cycles with 96.60 -99.37% fault coverage, while using 42.9 -47.18% fewer resources. Keywords: optical fiber networks, WDM networks, routing, fault tolerance, unicast, multicast communication INTRODUCTIONWe developed a novel method to deliver almost fault-tolerant capabilities of cycles in an optical network while significantly reducing the resource utilization when compared to the state-of-art techniques. Cycle-based routing can satisfy both dynamic point-to-point and multi-point optical communications. Cycles are created using quorums of nodes. Within a cycle, multicasts to all nodes in that cycle is possible. The quorum intersection property and the use of cyclic quorums sets provide all of the unicast capabilities. Exploiting the same properties we can achieve efficient broadcasts with O(√ ) multicasts.Optical networks are depended upon for high speed communications in distributed algorithms, as much as they are needed for the arbitrary point-to-point communications. Failures within a network are to be expected and can happen as much as every couple days. Protecting against these optical circuit faults is critical and there are many different approaches depending on the network needs and individual circumstances.For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Quorums sets for cycle-based routing to efficiently support arbitrary point-to-point and multi-point optical communication were first proposed in [1] with fault-tolerance analyzed in [2]. In this paper we apply the same established quorum set theory and add additional requirements to form suitable quorums for our optical network routing.The rest of the paper is organized as follows. Sections 2, and 3 establish the network model, node communication, and path routing / fault-tolerance. In Section 4, we discuss our application of the distributed efficiency of t...

In this paper we propose a generalized R redundancy cycle technique that provides optical networks almost fault-tolerant communications. More importantly, when applied using only single cycles rather than the standard paired cycles, the generalized R redundancy technique is shown to almost halve the necessary light-trail resources in the network while maintaining the fault-tolerance and dependability expected from cycle-based routing. For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Optimal communication quorum sets forming optical cycles based on light-trails have been shown to flexibly and efficiently route both point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle routing techniques will use pairs of cycles to achieve both routing and fault-tolerance, which uses substantial resources and creates the potential for underutilization. Instead, we intentionally utilize R redundancy within the quorum cycles for fault-tolerance such that every point-to-point communication pairs occur in at least R cycles. The result is a set of R = 3 redundant cycles with 93.23-99.34% fault coverage even with two simultaneous faults all while using 38.85-42.39% fewer resources.Comment: 7th International Workshop on Reliable Networks Design and Modeling, 5-7 Oct. 2015. arXiv admin note: substantial text overlap with arXiv:1608.05170, arXiv:1608.0516

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