Shortest path routing algorithm for hierarchical interconnection network-on-chip

Interconnection networks play a significant role in efficient on-chip communication for multicore systems. This paper introduces a new interconnection topology called the Hierarchical Cross Connected Recursive network (HCCR) and a shortest path routing algorithm for the HCCR. Proposed topology offers a high degree of regularity, scalability, and symmetry with a reduced number of links and node degree. A unique address encoding scheme is proposed for hierarchical graphical representation of HCCR networks, and based on this scheme a shortest path routing algorithm is devised. The algorithm requires 5(k-1) time where k=logn4-2 and k>0, in worst case to determine the next node along the shortest path

Design, Analysis and Computation in Wireless and Optical Networks

abstract: In the realm of network science, many topics can be abstracted as graph problems, such as routing, connectivity enhancement, resource/frequency allocation and so on. Though most of them are NP-hard to solve, heuristics as well as approximation algorithms are proposed to achieve reasonably good results. Accordingly, this dissertation studies graph related problems encountered in real applications. Two problems studied in this dissertation are derived from wireless network, two more problems studied are under scenarios of FIWI and optical network, one more problem is in Radio- Frequency Identification (RFID) domain and the last problem is inspired by satellite deployment. The objective of most of relay nodes placement problems, is to place the fewest number of relay nodes in the deployment area so that the network, formed by the sensors and the relay nodes, is connected. Under the fixed budget scenario, the expense involved in procuring the minimum number of relay nodes to make the network connected, may exceed the budget. In this dissertation, we study a family of problems whose goal is to design a network with “maximal connectedness” or “minimal disconnectedness”, subject to a fixed budget constraint. Apart from “connectivity”, we also study relay node problem in which degree constraint is considered. The balance of reducing the degree of the network while maximizing communication forms the basis of our d-degree minimum arrangement(d-MA) problem. In this dissertation, we look at several approaches to solving the generalized d-MA problem where we embed a graph onto a subgraph of a given degree. In recent years, considerable research has been conducted on optical and FIWI networks. Utilizing a recently proposed concept “candidate trees” in optical network, this dissertation studies counting problem on complete graphs. Closed form expressions are given for certain cases and a polynomial counting algorithm for general cases is also presented. Routing plays a major role in FiWi networks. Accordingly to a novel path length metric which emphasizes on “heaviest edge”, this dissertation proposes a polynomial algorithm on single path computation. NP-completeness proof as well as approximation algorithm are presented for multi-path routing. Radio-frequency identification (RFID) technology is extensively used at present for identification and tracking of a multitude of objects. In many configurations, simultaneous activation of two readers may cause a “reader collision” when tags are present in the intersection of the sensing ranges of both readers. This dissertation ad- dresses slotted time access for Readers and tries to provide a collision-free scheduling scheme while minimizing total reading time. Finally, this dissertation studies a monitoring problem on the surface of the earth for significant environmental, social/political and extreme events using satellites as sensors. It is assumed that the impact of a significant event spills into neighboring regions and there will be corresponding indicators. Careful deployment of sensors, utilizing “Identifying Codes”, can ensure that even though the number of deployed sensors is fewer than the number of regions, it may be possible to uniquely identify the region where the event has taken place.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Interconnection networks for parallel and distributed computing

Parallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))

RFID-Assisted wireless sensor networks for cardiac tele-healthcare

As the baby boomers head into old age, America will see a dramatic increase in the number of elderly patients admitted to healthcare facilities, such as nursing homes. Due to this rising elderly population, it will be difficult for nursing home personnel to monitor all patients at once. One way to cut down on the amount of supervision by the staff is for patients to administer their own medication. This leads to new problems though, as a patient incorrectly administering one of their many medications could lead to a disastrous end. Technology to wirelessly transmit a patient’s electrocardiogram (ECG) has also been implemented to reduce supervision. Wireless transmissions are infamous for their error rate, but the ECG is a sensitive signal where every second of data matters and cannot tolerate such losses. Additionally, such existing networks employ an expensive communication infrastructure. Due to this healthcare crisis, the ability for a device to remotely monitor a patient’s medication intake and transmit accurate ECG readings, while being cost efficient, is a major innovation. To combat this crisis, this thesis focuses on a multi-hop wireless sensor network (WSN) composed of many wearable sensors, one for each patient, that host a radio frequency identification (RFID) reader and are capable of RF communication. Each wearable device is also assumed to contain an ECG sensor, though this was not implemented in this work. The system is responsible for two distinct features. The first is remotely supervised patient medication intake via RFID and a central workstation/database. The second is the accurate remote transmission of a patient’s ECG using the extended Kalman filter (EKF) for wireless error recovery

Optimal Fault-Tolerant Spanners in Euclidean and Doubling Metrics: Breaking the Ω(log⁡n)\Omega(\log n) Lightness Barrier

An essential requirement of spanners in many applications is to be fault-tolerant: a $(1+\epsilon)$-spanner of a metric space is called (vertex) $f$-fault-tolerant ($f$-FT) if it remains a $(1+\epsilon)$-spanner (for the non-faulty points) when up to $f$ faulty points are removed from the spanner. Fault-tolerant (FT) spanners for Euclidean and doubling metrics have been extensively studied since the 90s. For low-dimensional Euclidean metrics, Czumaj and Zhao in SoCG'03 [CZ03] showed that the optimal guarantees $O(f n)$, $O(f)$ and $O(f^2)$ on the size, degree and lightness of $f$-FT spanners can be achieved via a greedy algorithm, which na\"{\i}vely runs in $O(n^3) \cdot 2^{O(f)}$ time. The question of whether the optimal bounds of [CZ03] can be achieved via a fast construction has remained elusive, with the lightness parameter being the bottleneck. Moreover, in the wider family of doubling metrics, it is not even clear whether there exists an $f$-FT spanner with lightness that depends solely on $f$ (even exponentially): all existing constructions have lightness $\Omega(\log n)$ since they are built on the net-tree spanner, which is induced by a hierarchical net-tree of lightness $\Omega(\log n)$. In this paper we settle in the affirmative these longstanding open questions. Specifically, we design a construction of $f$-FT spanners that is optimal with respect to all the involved parameters (size, degree, lightness and running time): For any $n$-point doubling metric, any $\epsilon > 0$, and any integer $1 \le f \le n-2$, our construction provides, within time $O(n \log n + f n)$, an $f$-FT $(1+\epsilon)$-spanner with size $O(f n)$, degree $O(f)$ and lightness $O(f^2)$.Comment: Abstract is shortened to meet arxiv's requirement on the number of character

Algorithms for security in robotics and networks

The dissertation presents algorithms for robotics and security. The first chapter gives an overview of the area of visibility-based pursuit-evasion. The following two chapters introduce two specific algorithms in that area. The algorithms are based on research done together with Dr. Giora Slutzki and Dr. Steven LaValle. Chapter 2 presents a polynomial-time algorithm for clearing a polygon by a single 1-searcher. The result is extended to a polynomial-time algorithm for a pair of 1-searchers in Chapter 3.;Chapters 4 and 5 contain joint research with Dr. Srini Tridandapani, Dr. Jason Jue and Dr. Michael Borella in the area of computer networks. Chapter 4 presents a method of providing privacy over an insecure channel which does not require encryption. Chapter 5 gives approximate bounds for the link utilization in multicast traffic

The power-series algorithm:A numerical approach to Markov processes

Abstract: The development of computer and communication networks and flexible manufacturing systems has led to new and interesting multidimensional queueing models. The Power-Series Algorithm is a numerical method to analyze and optimize the performance of such models. In this thesis, the applicability of the algorithm is extended. This is illustrated by introducing and analyzing a wide class of queueing networks with very general dependencies between the different queues. The theoretical basis of the algorithm is strengthened by proving analyticity of the steady-state distribution in light traffic and finding remedies for previous imperfections of the method. Applying similar ideas to the transient distribution renders new analyticity results. Various aspects of Markov processes, analytic functions and extrapolation methods are reviewed, necessary for a thorough understanding and efficient implementation of the Power-Series Algorithm.