The Distributed Spanning Tree Structure

International audienceSearch algorithms are a key issue to share resources in large distributed systems as peer networks. Several distributed interconnection structures and algorithms have already been studied in this context. With expanding ring algorithms, the efficiency of searches depends on the topology used to send query requests and on the dynamics of the structure. In this paper, we present an interconnection structure that limits the number of messages needed for search queries. This structure, called Distributed Spanning Tree (DST), defines each node as the root of a spanning tree. So, it behaves as a tree for the number of messages but it balances the load generated by the requests among computers and, thus, it avoids to overload the root~node. This structure is scalable because it only needs a logarithmic memory space per computer to be maintained. A formal and practical description of the structure is presented and we describe traversal algorithms. Simulations show that DST based searches behave better than randomly generated graphs and trees as it generates less messages to query all computers while avoiding the tree bottlenecks

I/O embedding and broadcasting in star interconnection networks

The issues of communication between a host or central controller and processors, in large interconnection networks are very important and have been studied in the past by several researchers. There is a plethora of problems that arise when processors are asked to exchange information on parallel computers on which processors are interconnected according to a specific topology. In robust networks, it is desirable at times to send (receive) data/control information to (from) all the processors in minimal time. This type of communication is commonly referred to as broadcasting. To speed up broadcasting in a given network without modifying its topology, certain processors called stations can be specified to act as relay agents. In this thesis, broadcasting issues in a star-based interconnection network are studied. The model adopted assumes all-port communication and wormhole switching mechanism. Initially, the problem treated is one of finding the minimum number of stations required to cover all the nodes in the star graph with i-adjacency. We consider 1-, 2-, and 3-adjacencies and determine the upper bound on the number of stations required to cover the nodes for each case. After deriving the number of stations, two algorithms are designed to broadcast the messages first from the host to stations, and then from stations to remaining nodes; In addition, a Binary-based Algorithm is designed to allow routing in the network by directly working on the binary labels assigned to the star graph. No look-up table is consulted during routing and minimum number of bits are used to represent a node label. At the end, the thesis sheds light on another algorithm for routing using parallel paths in the star network

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms

Topological Properties and Broadcasting Algorithmsof the Generalized-Star Cube

Abstract—In this research, another version of the star cube called the generalized-star cube, GSC(n, k, m), is presented as a three level interconnection topology. GSC(n, k, m) is a product graph of the (n, k)-star graph and the m-dimensional hypercube (m-cube). It can be constructed in one of two ways: to replace each node in an m-cube with an (n, k)-star graph, or to replace each node in an (n, k)-star graph with an m-cube. Because there are three parameters m, n, and k, the network size of GSC(n, k, m) can be changed more flexibly than the star graph, star-cube, and (n, k)-star graph. We first investigate the topological properties of the GSC(n, k, m), such as the node degree, diameter, average distance, and cost. Also, the regularity and node symmetry of the GSC(n, k, m) are derived.Then, we illustrate the broadcasting algorithms for both of the single-port and all-port models. To develop these algorithms, we use the spanning binomial tree, the neighbourhood broadcasting algorithm, and the minimum dominating set. The complexities of the broadcasting algorithms are also examined

Efficient hypercube communications

Hypercube algorithms may be developed for a variety of communication-intensive tasks such as sending a message from one node to another, broadcasting a message from one node to all others, broadcasting a message from each node to all others, all-to-all personalized communication, one-to-all personalized communication, and exchanging messages between nodes via fixed permutations. All these communication patterns are special cases of many-to-many personalized communication. The problem of many-to-many personalized communication is investigated here. Two routing algorithms for many-to-many personalized communication are presented here. The algorithms proposed yield very high performance with respect to the number of time steps and packet transmissions. The first algorithm yields high performance through attempts to equibalance the number of messages at intermediate nodes. This technique tries to avoid creating a bottleneck at any node and thus reduces the total communication time. The second algorithm yields high performance through one-step time-lookahead equibalancing. It chooses from the candidate intermediate nodes the one which will probably have the minimum number of messages in the next cycle

Optical control plane: theory and algorithms

In this thesis we propose a novel way to achieve global network information dissemination in which some wavelengths are reserved exclusively for global control information exchange. We study the routing and wavelength assignment problem for the special communication pattern of non-blocking all-to-all broadcast in WDM optical networks. We provide efficient solutions to reduce the number of wavelengths needed for non-blocking all-to-all broadcast, in the absence of wavelength converters, for network information dissemination. We adopt an approach in which we consider all nodes to be tap-and-continue capable thus studying lighttrees rather than lightpaths. To the best of our knowledge, this thesis is the first to consider “tap-and-continue” capable nodes in the context of conflict-free all-to-all broadcast. The problem of all to-all broadcast using individual lightpaths has been proven to be an NP-complete problem [6]. We provide optimal RWA solutions for conflict-free all-to-all broadcast for some particular cases of regular topologies, namely the ring, the torus and the hypercube. We make an important contribution on hypercube decomposition into edge-disjoint structures. We also present near-optimal polynomial-time solutions for the general case of arbitrary topologies. Furthermore, we apply for the first time the “cactus” representation of all minimum edge-cuts of graphs with arbitrary topologies to the problem of all-to-all broadcast in optical networks. Using this representation recursively we obtain near-optimal results for the number of wavelengths needed by the non-blocking all-to-all broadcast. The second part of this thesis focuses on the more practical case of multi-hop RWA for non- blocking all-to-all broadcast in the presence of Optical-Electrical-Optical conversion. We propose two simple but efficient multi-hop RWA models. In addition to reducing the number of wavelengths we also concentrate on reducing the number of optical receivers, another important optical resource. We analyze these models on the ring and the hypercube, as special cases of regular topologies. Lastly, we develop a good upper-bound on the number of wavelengths in the case of non-blocking multi-hop all-to-all broadcast on networks with arbitrary topologies and offer a heuristic algorithm to achieve it. We propose a novel network partitioning method based on “virtual perfect matching” for use in the RWA heuristic algorithm

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area

Robust Localization from Incomplete Local Information

We consider the problem of localizing wireless devices in an ad-hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimation of where wireless devices are located is crucial in wireless network applications including environment monitoring, geographic routing and topology control. When the positions of the devices are unknown and only local distance information is given, we need to infer the positions from these local distance measurements. This problem is particularly challenging when we only have access to measurements that have limited accuracy and are incomplete. We consider the extreme case of this limitation on the available information, namely only the connectivity information is available, i.e., we only know whether a pair of nodes is within a fixed detection range of each other or not, and no information is known about how far apart they are. Further, to account for detection failures, we assume that even if a pair of devices is within the detection range, it fails to detect the presence of one another with some probability and this probability of failure depends on how far apart those devices are. Given this limited information, we investigate the performance of a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a distributed positioning algorithm, introduced by Savarese et al., called HOP-TERRAIN. In particular, for a network consisting of n devices positioned randomly, we provide a bound on the resulting error for both algorithms. We show that the error is bounded, decreasing at a rate that is proportional to R/Rc, where Rc is the critical detection range when the resulting random network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure