Symmetric Interconnection Networks from Cubic Crystal Lattices

Torus networks of moderate degree have been widely used in the supercomputer industry. Tori are superb when used for executing applications that require near-neighbor communications. Nevertheless, they are not so good when dealing with global communications. Hence, typical 3D implementations have evolved to 5D networks, among other reasons, to reduce network distances. Most of these big systems are mixed-radix tori which are not the best option for minimizing distances and efficiently using network resources. This paper is focused on improving the topological properties of these networks. By using integral matrices to deal with Cayley graphs over Abelian groups, we have been able to propose and analyze a family of high-dimensional grid-based interconnection networks. As they are built over $n$-dimensional grids that induce a regular tiling of the space, these topologies have been denoted \textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling symmetric 3D networks. Other higher dimensional networks can be composed over these graphs, as illustrated in this research. Easy network partitioning can also take advantage of this network composition operation. Minimal routing algorithms are also provided for these new topologies. Finally, some practical issues such as implementability and preliminary performance evaluations have been addressed

A reliable and resource aware framework for data dissemination in wireless sensor networks

Distinctive from traditional wireless ad hoc networks, wireless sensor networks (WSN) comprise a large number of low-cost miniaturized nodes each acting autonomously and equipped with short-range wireless communication mechanism, limited memory, processing power, and a physical sensing capability. Since sensor networks are resource constrained in terms of power, bandwidth and computational capability, an optimal system design radically changes the performance of the sensor network. Here, a comprehensive information dissemination scheme for wireless sensor networks is performed. Two main research issues are considered: (1) a collaborative flow of information packet/s from the source to sink and (2) energy efficiency of the sensor nodes and the entire system. For the first issue, we designed and evaluated a reactive and on-demand routing paradigm for distributed sensing applications. We name this scheme as IDLF-Information Dissemination via Label ForwarDing IDLF incorporates point to point data transmission where the source initiates the routing scheme and disseminates the information toward the sink (destination) node. Prior to transmission of actual data packet/s, a data tunnel is formed followed by the source node issuing small label information to its neighbors locally. These labels are in turn disseminated in the network. By using small size labels, IDLF avoids generation of unnecessary network traffic and transmission of duplicate packets to nodes. To study the impact of node failures and to improve the reliability of the network, we developed another scheme which is an extension to IDLF. This new scheme, RM-IDLF - Reliable Multipath Information dissemination by Label Forwarding, employ an alternate disjoint path. This alternate path scheme (RM-IDLF) may have a higher path cost in terms of energy consumption, but is more reliable in terms of data packet delivery to sink than the single path scheme (IDLF). In the latter scheme, the protocol establishes multiple (alternate) disjoint path/s from source to destination with negligible control overhead to balance load due to heavy data traffic among intermediate nodes from source to the destination. Another point of interest in this framework is the study of trade-offs between the achieved routing reliability using multiple disjoint path routing and extra energy consumption due to the use of additional path/s. Also, the effect of the failed nodes on the network performance is evaluated within the sensor system; Performance of the label dissemination scheme is evaluated and compared with the classic flooding and SPIN. (Abstract shortened by UMI.)

Fairness Comparison of TCP Variants over Proactive and Reactive Routing Protocol in MANET

Mobile ad hoc networks (MANETs) are applicable in an infrastructureless environment where the mobile devices act as routers and intermediate nodes are used to transfer segments to their final destination. As Transmission control protocol (TCP) was originated for Internet with fundamentally different properties, faces serious challenges when used in mobile ad hoc networks. TCP functionality degrades, due to special properties of MANET such as route failure because of significant change of network topology and link errors. TCP uses Congestion Control Algorithms; TCP Vegas is one of them which claim to have better throughput comparing with other TCP variants in a wired network. Fairness issues of TCP Variants in MANET including existing routing protocol are still unsolved. To determine the best TCP Variants in MANET environment over renowned routing protocol is the main objective of this paper. A Study on the throughput fairness of TCP Variants namely, Vegas, Reno, New Reno, SACK, FACK, and Cubic are performed via simulation experiment using network simulator (ns-2) over existing routing protocol, named, AODV, AOMDV, DSDV, and DSR. This fairness evaluation of TCP flows arranged a contrast medium for the TCP Variants using stated routing protocol in MANET. However, TCP Vegas obtain unfair throughput in MANET. The simulation results show that TCP Reno outperforms other TCP variants under DSDV routing protocol

The cavity approach for Steiner trees packing problems

The Belief Propagation approximation, or cavity method, has been recently applied to several combinatorial optimization problems in its zero-temperature implementation, the max-sum algorithm. In particular, recent developments to solve the edge-disjoint paths problem and the prize-collecting Steiner tree problem on graphs have shown remarkable results for several classes of graphs and for benchmark instances. Here we propose a generalization of these techniques for two variants of the Steiner trees packing problem where multiple "interacting" trees have to be sought within a given graph. Depending on the interaction among trees we distinguish the vertex-disjoint Steiner trees problem, where trees cannot share nodes, from the edge-disjoint Steiner trees problem, where edges cannot be shared by trees but nodes can be members of multiple trees. Several practical problems of huge interest in network design can be mapped into these two variants, for instance, the physical design of Very Large Scale Integration (VLSI) chips. The formalism described here relies on two components edge-variables that allows us to formulate a massage-passing algorithm for the V-DStP and two algorithms for the E-DStP differing in the scaling of the computational time with respect to some relevant parameters. We will show that one of the two formalisms used for the edge-disjoint variant allow us to map the max-sum update equations into a weighted maximum matching problem over proper bipartite graphs. We developed a heuristic procedure based on the max-sum equations that shows excellent performance in synthetic networks (in particular outperforming standard multi-step greedy procedures by large margins) and on large benchmark instances of VLSI for which the optimal solution is known, on which the algorithm found the optimum in two cases and the gap to optimality was never larger than 4 %

CLEX: Yet Another Supercomputer Architecture?

We propose the CLEX supercomputer topology and routing scheme. We prove that CLEX can utilize a constant fraction of the total bandwidth for point-to-point communication, at delays proportional to the sum of the number of intermediate hops and the maximum physical distance between any two nodes. Moreover, % applying an asymmetric bandwidth assignment to the links, all-to-all communication can be realized $(1+o(1))$-optimally both with regard to bandwidth and delays. This is achieved at node degrees of $n^{\varepsilon}$, for an arbitrary small constant $\varepsilon\in (0,1]$. In contrast, these results are impossible in any network featuring constant or polylogarithmic node degrees. Through simulation, we assess the benefits of an implementation of the proposed communication strategy. Our results indicate that, for a million processors, CLEX can increase bandwidth utilization and reduce average routing path length by at least factors $10$ respectively $5$ in comparison to a torus network. Furthermore, the CLEX communication scheme features several other properties, such as deadlock-freedom, inherent fault-tolerance, and canonical partition into smaller subsystems

Joint optimization for wireless sensor networks in critical infrastructures

Energy optimization represents one of the main goals in wireless sensor network design where a typical sensor node has usually operated by making use of the battery with limited-capacity. In this thesis, the following main problems are addressed: first, the joint optimization of the energy consumption and the delay for conventional wireless sensor networks is presented. Second, the joint optimization of the information quality and energy consumption of the wireless sensor networks based structural health monitoring is outlined. Finally, the multi-objectives optimization of the former problem under several constraints is shown. In the first main problem, the following points are presented: we introduce a joint multi-objective optimization formulation for both energy and delay for most sensor nodes in various applications. Then, we present the Karush-Kuhn-Tucker analysis to demonstrate the optimal solution for each formulation. We introduce a method of determining the knee on the Pareto front curve, which meets the network designer interest for focusing on more practical solutions. The sensor node placement optimization has a significant role in wireless sensor networks, especially in structural health monitoring. In the second main problem of this work, the existing work optimizes the node placement and routing separately (by performing routing after carrying out the node placement). However, this approach does not guarantee the optimality of the overall solution. A joint optimization of sensor placement, routing, and flow assignment is introduced and is solved using mixed-integer programming modelling. In the third main problem of this study, we revisit the placement problem in wireless sensor networks of structural health monitoring by using multi-objective optimization. Furthermore, we take into consideration more constraints that were not taken into account before. This includes the maximum capacity per link and the node-disjoint routing. Since maximum capacity constraint is essential to study the data delivery over limited-capacity wireless links, node-disjoint routing is necessary to achieve load balancing and longer wireless sensor networks lifetime. We list the results of the previous problems, and then we evaluate the corresponding results

PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFS-traversal of the graph. PReaCH-indices significantly outperform previous data structures with comparable preprocessing cost. Methods with faster queries need significantly more preprocessing time in particular for the most difficult instances

Exact Distance Oracles for Planar Graphs

We present new and improved data structures that answer exact node-to-node distance queries in planar graphs. Such data structures are also known as distance oracles. For any directed planar graph on n nodes with non-negative lengths we obtain the following: * Given a desired space allocation $S\in[n\lg\lg n,n^2]$, we show how to construct in $\tilde O(S)$ time a data structure of size $O(S)$ that answers distance queries in $\tilde O(n/\sqrt S)$ time per query. As a consequence, we obtain an improvement over the fastest algorithm for k-many distances in planar graphs whenever $k\in[\sqrt n,n)$. * We provide a linear-space exact distance oracle for planar graphs with query time $O(n^{1/2+eps})$ for any constant eps>0. This is the first such data structure with provable sublinear query time. * For edge lengths at least one, we provide an exact distance oracle of space $\tilde O(n)$ such that for any pair of nodes at distance D the query time is $\tilde O(min {D,\sqrt n})$. Comparable query performance had been observed experimentally but has never been explained theoretically. Our data structures are based on the following new tool: given a non-self-crossing cycle C with $c = O(\sqrt n)$ nodes, we can preprocess G in $\tilde O(n)$ time to produce a data structure of size $O(n \lg\lg c)$ that can answer the following queries in $\tilde O(c)$ time: for a query node u, output the distance from u to all the nodes of C. This data structure builds on and extends a related data structure of Klein (SODA'05), which reports distances to the boundary of a face, rather than a cycle. The best distance oracles for planar graphs until the current work are due to Cabello (SODA'06), Djidjev (WG'96), and Fakcharoenphol and Rao (FOCS'01). For $\sigma\in(1,4/3)$ and space $S=n^\sigma$, we essentially improve the query time from $n^2/S$ to $\sqrt{n^2/S}$.Comment: To appear in the proceedings of the 23rd ACM-SIAM Symposium on Discrete Algorithms, SODA 201