CONCURRENT GEOMETRIC ROUTING A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Jordan Matthew Adamek June 2017 Dissertation written by Jordan Matthew Adamek B.S., Kent State University, 2013 M.A., Kent State University, 2015 Ph.D., Kent State University, 2017 Approved by , Chair, Doctoral Dissertation Committee Dr. Mikhail Nesterenko , Members, Doctoral Dissertation Committee Dr. Gokarna Sharma Dr. Hassan Peyravi Dr. Volodymyr Andriyevskyy Dr. Andrew Tonge Accepted by , Chair, Department of Computer Science Dr. Javed Khan , Dean, College of Arts and Sciences Dr. James Blank TABLE OF CONTENTS LIST OF FIGURES . v Acknowledgements . vii Dedication . viii 1 Introduction . 1 1.1 Motivation . 1 1.2 Literature Review . 8 1.3 Notation and Definitions . 18 2 Geocasting . 22 2.1 Algorithm Descriptions . 22 2.2 Correctness Proofs . 27 2.3 Abstract Simulation . 31 2.4 Concrete Simulation . 35 2.5 Efficiency Bounds . 37 3 Multicasting . 45 3.1 MCFR, Algorithm Description . 46 3.2 Correctness Proof and Efficiency Bounds . 49 3.3 Abstract Simulation . 54 iii 3.4 Concrete Simulation . 57 3.5 Conclusion . 62 4 Multisource broadcast . 63 4.1 Simulation . 65 4.2 Conclusion . 65 5 Conclusions . 67 BIBLIOGRAPHY . 68 iv LIST OF FIGURES 1 Face traversal in GFG. 3 2 Example operation of face routing. 4 3 Example graph for 2E message cost in SPG. 16 4 Examples of inner edges as entry edges in BM. 17 5 SF pseudocode. 23 6 SPG pseudocode. 24 7 Example computation of SPG. 26 8 Abstract Simulation: Message cost normalized to geocast region size. 33 9 Abstract Simulation: Arrival latency normalized to optimal path (path stretch). 34 10 Concrete simulation: Comparing SPG with stateful flooding (FLOOD) and GFG plus flooding in the geocast area (GFG+SF). 42 11 Concrete simulation: Comparing SPG delivery at different signal strengths . 43 12 Concrete simulation: Comparing SPG performance at different signal strengths . 44 13 Estimating the number of devices in the geocast region. 44 14 MCFR pseudocode. 46 15 MCFR operation example. 48 16 Covering the source-target Steiner hull with unit circles. Illustration for the proof of Theorem 8. 48 17 Abstract Simulation: Message cost normalized to number of destinations. 55 18 Abstract Simulation: Arrival latency normalized to optimal path (path stretch). 56 v 19 Time to live evaluation for MCFR, Steiner Tree, 15 dBm. 59 20 Delivery ratio. 59 21 Latency. 60 22 Message cost. 61 23 Concrete simulation: performance of flooding under changing signal strength. 64 vi Acknowledgements This dissertation is the product of years of hard work by several key individuals. Dr. Mikhail Nesterenko oversaw and guided all research and simulation efforts, and contributed the major por- tion of all original algorithm designs. James Robinson implemented the following modules for concrete geocast and multicast simulations in WorldSENS: geocasting and multicasting applica- tion modules, SPG (both versions) and MCFR routing modules, supplementary code to compute minimum Euclidean spanning tree, breadth-first search, connected dominating set, Dijkstra’s al- gorithm and Gabriel graph. James Robinson also researched and implemented the best simulation configuration to achieve a realistic communication model. Dr. Gokarna Sharma provided excellent algorithmic counsel, especially in regards to message loss considerations. Dr. Sebastien´ Tixeuil provided advice and criticism throughout the geocasting and multicasting research efforts. Most notably, Dr. Tixeuil suggested the use of WorldSENS to accomplish our concrete simulation goals, and provided the necessary materials to obtain and research the simulator. vii I dedicate this work to my family and my advisor, all of whom have unfailingly supported me through many trying years of personal and academic growth. viii CHAPTER 1 Introduction 1.1 Motivation Wireless devices have become ubiquitous. They are shown to be of great practical value for such applications as environmental observation [61,82], natural disaster warning [13,25], and even vehicular traffic monitoring services [16, 88, 89]. Such applications may demand a great number of often unattended inexpensive devices frequently deployed in volatile and even hostile environ- ments. Such devices may be unable to rely on a central infrastructure for message routing due to scale and frequency of topological change, and must rely on an ad hoc approach to communi- cation. Furthermore, these devices may be locally powered by a limited source such as a small battery. Hence, the problem of scalable, reliable and efficient ad hoc networking for resource poor devices comes to the fore. Early ad hoc routing algorithms are typically routing-table based [34, 41, 70]. These routing tables have to be maintained at the devices. Source-routing algorithms [41] require the message to carry its entire route. Routing tables allow efficient message navigation. Source routing is robust as it eliminates a large number of problems such as counting-to-infinity [58, 70]. However, maintenance of such routing tables for a large-scale network may be resource intensive. This problem is exacerbated if the network topology changes frequently as it does in wireless sensor networks or vehicular networks. In source-routing, the size of the message increases with the size of the network. This may not scale well either. 1 2 In this dissertation, we are exploring routing solutions that do not require routing tables or unlimited-size messages. Flooding. One of the simplest routing-table-free and constant-message-size routing algorithms is controlled flooding, where each device retransmits the message to all its neighbors. Flooding potentially involves all communication devices of the network and, therefore, does not scale well. However, if the flooding area is limited, it becomes a useful strategy. Classic flooding is stateful as each device needs to store information about the transmission to prevent message resends. Main- taining state of a message transmission consumes resources and does not scale well. In a stateless algorithm, an intermediate device does not retain message transmission information after it for- wards the message. This feature has good scalability and fault-tolerance properties, but it prohibits such useful stateful routing techniques as backpressure [65] routing or exploring the network in a depth-first manner. In this dissertation, we study stateless routing; in particular, stateless flooding. Geometric routing. Another attractive stateless solution is geometric routing. Geometric routing is navigating a message from the sender to the destination on the basis of the geometric locations of the devices in the communication network. These locations may be physical coordinates obtained, for example, from GPS, or virtual coordinates computed by the devices [39, 44, 46, 48, 64]. For example, the simplest form of geometric routing is greedy routing. In greedy routing [26], each intermediate device forwards the message to its neighbor that is the closest to the destination. Ge- ometric routing is stateless, it has constant-message size and it does not require routing tables. The only routing information required for each device is the coordinates of its immediate neighbors. 3 Figure 1: Face traversal in GFG. Face routing. Pure greedy routing fails if the device encounters a local minimum: a device that does not have neighbors closer to the destination than itself. A geometric routing algorithm, such as the classic GFG [8, 22], routes the message in greedy mode until a local minimum is encountered. The algorithm then switches to recovery mode which usually involves traversing faces of a planar subgraph of the original communication graph. See Figure 1 for an example message navigation in GFG. In a finite planar graph, the number of faces is limited. This number is further reduced by restricting the message to faces which cross a source-destination segment of the line. A face may be traversed using right-hand- or left-hand-rule. Which results in counter- and clockwise face traversal direction. Each node may determine the message traversal direction locally. When a recovery mode message traverses an edge which intersects the source-destination line, it switches faces. The messages continues routing in recovery mode until it gets closer to the destination than the last encountered local minimum. The message then switches back to greedy mode and the process repeats. This traversal, therefore, guarantees delivery to the destination. Sequential and concurrent routing. Typical greedy and face routing algorithms are sequential. 4 Figure 2: Example operation of face routing. In a sequential algorithm, a single message is sent from source to the destination. A sequential solution yields a low message cost, but may discover suboptimal paths and is highly susceptible to message loss. Alternatively, concurrent routing solutions such as flooding use multiple messages to traverse faces, and may thus trade a higher message cost for quicker delivery and higher robustness. Refer to Figure 1.1 for illustration of the operation of the unicasting concurrent face routing algorithm CFR [18]. The source s needs to send a message to destination d. The source s initiates the traversal of the face that intersects the sd-segment in two opposite directions at once. Specifi- cally, s sends left-hand-rule message 1 and right-hand-rule message 2.A juncture has at least one edge that intersects the sd-segment of the line. Note that the source s is a juncture as well: it lies on the sd-segment. If a message reaches a juncture, the juncture forwards the message but also initiates concurrent traversal of all other adjacent faces that intersect the sd-segment. For example, once 2 reaches device i, it forwards 2 to f and sends a left-hand-rule message 3 to f as well as right-hand-rule message 4 to j. Two messages are mates if they traverse the same face in opposite directions. If they meet at one device, they are destroyed. Thus, when receiving a message, each device checks its send queue for the mate of the message.