Design and analysis of dynamic leader election protocols in broadcast networks

Summary.  The well-known problem of leader election in distributed systems is considered in a dynamic context where processes may participate and crash spontaneously. Processes communicate by means of buffered broadcasting as opposed to usual point-to-point communication. In this paper we design a leader election protocol in such a dynamic context. As the problem at hand is considerably complex we develop the protocol in three steps. In the initial design processes are considered to be perfect and a leader is assumed to be present initially. In the second protocol, the assumption of an initial leader is dropped. This leads to a symmetric protocol which uses an (abstract) timeout mechanism to detect the absence of a leader. Finally, in the last step of the design processes may crash without giving any notification of other processes. The worst case message complexity of all protocols is addressed. A formal approach to the specification and verification of the leader election protocols is adopted. The requirements are specified in a property-oriented way and the protocols are denoted by means of extended finite state machines. It is proven using linear-time temporal logic that the fault-tolerant protocol satisfies its requirements. Received: September 1993 / Revised: September 1995     

Performing work in broadcast networks

We consider the problem of how to schedule t similar and independent tasks to be performed in a synchronous distributed system of p stations communicating via multiple-access channels. Stations are prone to crashes whose patterns of occurrence are specified by adversarial models. Work, defined as the number of the available processor steps, is the complexity measure. We consider only reliable algorithms that perform all the tasks as long as at least one station remains operational. It is shown that every reliable algorithm has to perform work Ω(t+p√t) even when no failures occur. An optimal deterministic algorithm for the channel with collision detection is developed, which performs work (t+p√t). Another algorithm, for the channel without collision detection, performs work (t+p √t+ p min {f,t}), where f < p is the number of failures. This algorithm is proved to be optimal, provided that the adversary is restricted in failing no more than f stations. Finally, we consider the question if randomization helps against weaker adversaries for the channel without collision detection. A randomized algorithm is developed which performs the expected minimum amount (t+p√t) of work, provided that the adversary may fail a constant fraction of stations and it has to select failure-prone stations prior to the start of an execution of the algorithm. The work of the first author is supported by the NSF Grant 0310503. A preliminary version of this paper appeared as “The do-all problem in broadcast networks,” in Proceedings, 20th ACM Symposium on Principles of Distributed Computing, Newport, Rhode Island, 2001, pp. 117–126.     

Distributed election in complete networks

An improved version of Afek and Gafni's synchronous algorithm for distributed election in complete networks is given and anO(n) expected message complexity is shown. M.Y. Chan received her Ph.D. in 1988 from the University of Hong Kong, and her M.S. and B.A. degrees in computer science from the University of California, San Diego in 1980 and 1981, respectively. She is currently an Assistant Professor at the University of Texas at Dallas. Francis Y.L. Chin (S71-M76-SM85) received the B.Sc. degree in engineering science from the University of Toronto, Toronto, Canada, in 1972, and the M.S., M.A., and Ph.D. degrees in electrical engineering and computer science from Princeton University, New Jersey, in 1974, 1975, and 1976, respectively. Since 1975, he has taught at the University of Maryland, Baltimore Country, University of California, San Diego, University of Alberta, and Chinese University of Hong Kong. He is currently Head of the Department of Computer Science, University of Hong Kong. He has served as a program co-chairman of the 1988 International Conference on Computer Processing of Chinese and Oriental Languages (Toronto) and the International Computer Science Conference '88 (Hong Kong). His current research interests include algorithm design and analysis, parallel and distributed computing.     

Weighted broadcast in linear radio networks

The weighted version of the broadcast range assignment problem in ad hoc wireless network is studied. Efficient algorithms are presented for the unbounded and bounded-hop broadcast problems for the linear radio network, where radio stations are placed on a straight line. For the unbounded case of the problem, the proposed algorithm runs in O(n²) time and using O(n) space, where n is the number of radio stations in the network. For the h-hop broadcast problem, the time and space complexities of our algorithm are O(hn²logn) and O(hn), respectively. This improves time complexity of the existing results for the same two problems by a factor of n and , respectively [C. Ambuhl, A.E.F. Clementi, M.D. Ianni, G. Rossi, A. Monti, R. Silvestri, The range assignment problem in non-homogeneous static ad hoc networks, in: Proc. 18th Int. Parallel and Distributed Precessing Symposium, 2004].     

Centralized asynchronous broadcast in radio networks

We study asynchronous broadcasting in packet radio networks. A radio network is represented by a directed graph, in which one distinguished source node stores a message that needs to be disseminated among all the remaining nodes. An asynchronous execution of a protocol is a sequence of events, each consisting of simultaneous deliveries of messages. The correctness of protocols is considered for specific adversarial models defined by restrictions on events the adversary may schedule. A protocol specifies how many times the source message is to be retransmitted by each node. The total number of transmissions over all the nodes is called the work of the broadcast protocol; it is used as complexity measure. We study computational problems, to be solved by deterministic centralized algorithms, either to find a broadcast protocol or to verify the correctness of a protocol, for a given network. The amount of work necessary to make a protocol correct may have to be exponential in the size of network. There is a polynomial-time algorithm to find a broadcast protocol for a given network. We show that certain problems about broadcasting protocols for given networks are complete in NP and co-NP complexity classes.     

Key continual-leakage resilient broadcast cryptosystem from dual system in broadcast networks

In order to tolerate possible leakage of secret keys, leakage-resilient cryptosystem models a class of attractive leakage output by allowing an adversary to provide any computable leakage function and learning the partial keys or other possible intemal states from the output of function. In this work, we present an adaptively secure broadcast encryption resilient to key continual leakage in the standard model. Our scheme provides the tolerance of continual leakage, in which any user can generate multiple private keys per user by periodically updating the key. We use the dual system encryption mechanism to implement the leakage resilience and adaptive security, and intrinsically set an algorithm to refresh a key and produce a same distributed new key. We also give the evaluation of the leakage bound and leakage fraction, and the simulations show that our scheme can tolerate about 71% leakage fraction with 3.34× 10^-52 failure probability in standard 80-bit security level when we adjust the leakage factor to allow the private key to be 100 Kb.     

Energy efficient all-to-all broadcast in all-wireless networks

All-to-all broadcast is a communication pattern in which every node initiates a broadcast. In this paper, we investigate the problem of building a unique cast tree of minimum total energy, which we call Minimum Unique Cast (MUC) tree, to be used for all-to-all broadcast. The MUC tree is unoriented and unrooted. We study three known heuristics for the minimum-energy broadcast problem: the Broadcast Incremental Power (BIP) algorithm, the Wireless Multicast Advantage-conforming Minimum Spanning Tree (WMA-conforming MST) algorithm, and the Iterative Maximum-Branch Minimization (IMBM) algorithm. Experimental results conducted on various types of networks are reported. We show that neither of these methods is best overall for building all-to-all broadcast trees.     

Static analysis of topology-dependent broadcast networks

Broadcast semantics poses significant challenges over point-to-point communication when it comes to formal modelling and analysis. Current approaches to analysing broadcast networks have focused on fixed connectivities, but this is unsuitable in the case of wireless networks where the dynamically changing network topology is a crucial ingredient. In this paper, we develop a static analysis that automatically constructs an abstract transition system, labelled by actions and connectivity information, to yield a mobility-preserving finite abstraction of the behaviour of a network expressed in a process calculus with asynchronous local broadcast. Furthermore, we use model checking based on a 3-valued temporal logic to distinguish network behaviour which differs under changing connectivity patterns.     

Optimizing responses to broadcast messages in radio networks

Algorithms to optimize the performance of response traffic for broadcast messages in a packet-switched radio network are studied. The situation considered here involves a source node sending a broadcast message to all destinations and collecting positive response packets from these destinations in a fully connected packet radio network. The exact value of the number of destination nodes is unknown. A contention-based two-level protocol is described. Based on the protocol, an optimization problem is formulated in order to minimize the time for the source node to receive all the responses. Several algorithms are presented and numerical results of the corresponding optimization problems are obtained. These optimization problems are treated by the methods of dynamic programming. An extension of the basic scheme—multicast instead of full broadcast message—is also studied.This work was supported by the US Army Research Office under Contract No. DAAG29-84-K-0084.     

Reliable networks with unreliable sensors

Wireless sensor networks (WSNs) deployed in hostile environments suffer from a high rate of node failure. We investigate the effect of such failure rate on network connectivity. We provide a formal analysis that establishes the relationship between node density, network size, failure probability, and network connectivity. We show that large networks can maintain connectivity despite a significantly high probability of node failure. We derive mathematical functions that provide lower bounds on network connectivity in WSNs. We compute these functions for some realistic values of node reliability, area covered by the network, and node density, to show that, for instance, networks with over a million nodes can maintain connectivity with a probability exceeding 95% despite node failure probability exceeding 53%.     

A recursion-based broadcast paradigm in wormhole routed networks

A novel broadcast technique for wormhole-routed parallel computers based on recursion is presented in this paper. It works by partitioning the interconnection graph into a number of higher-level subgraphs. Then, we identify the transmission subgraph (TSG) in each subgraph. Both the higher-level subgraphs and the TSGs are recursively defined, i.e., we split each level i subgraph into several level i+1 subgraphs and identify-level i+1 TSGs accordingly. We first split and scatter the source message into the TSG of the original graph. Next, in each recursive round message transmissions are from lower-level TSGs to higher-level TSGs and all transmissions at the same level happen concurrently. The algorithm proceeds recursively from lower-level subgraphs to higher level subgraphs until each highest-level subgraph (a single node) gets the complete message. We have applied this general paradigm to a number of topologies including two or higher dimension mesh/torus and hypercube. Our results show considerable improvements over all other algorithms for a wide range of message sizes under both one-port and all-port models.     

Optimizing responses to broadcast messages in radio networks

Algorithms to optimize the performance of response traffic for broadcast messages in a packet-switched radio network are studied. The situation considered here involves a source node sending a broadcast message to all destinations and collecting positive response packets from these destinations in a fully connected packet radio network. The exact value of the number of destination nodes is unknown. A contention-based two-level protocol is described. Based on the protocol, an optimization problem is formulated in order to minimize the time for the source node to receive all the responses. Several algorithms are presented and numerical results of the corresponding optimization problems are obtained. These optimization problems are treated by the methods of dynamic programming. An extension of the basic scheme—multicast instead of full broadcast message—is also studied.     

On the number of broadcast schemes in networks

Broadcasting is the process of spreading one piece of information among a group of individuals connected by an interconnection network. In this paper we give exact lower and upper bounds for the number of broadcast schemes in arbitrary networks. Also, we give the exact value for complete bipartite graphs and an upper bound for regular networks. Based on the counting method we describe a new random algorithm for broadcasting in networks.     

Reliable and efficient communications in sensor networks

Wireless sensor networks are inherently plagued by problems of node failure, interference to communications from environmental noise and energy-limited sensor motes. These problems pose conflicting issues in the design of suitable routing protocols. Several existing reliable routing protocols exploit message broadcast redundancy and hop count as routing metrics and their performance trade-offs are revealed during simulation. In this paper, we study and analyse related design issues in proposed efficient and reliable routing protocols that attempt to achieve reliable and efficient communication performance in both single- and multi-hub sensor networks. Simulation results of four such routing protocols show that routing performance depends more on optimal (near-optimal) routing in single hub than in multi-hub networks. Our work also shows that optimal (near-optimal) routing is better achieved when historical metrics like packet distance traversed and transmission success are also considered in the routing protocol design.     

Multihop all-to-all broadcast on WDM optical networks

Wavelength-division multiplexing (WDM) optical networks provide huge bandwidth by allowing multiple data streams transmitted simultaneously along the same optical fiber, with each stream assigned a distinct wavelength. A key issue on WDM optical networks is to minimize the number of wavelengths for communications. All-to-all broadcast (gossiping) is a fundamental communication application on computer/communication networks. It is known that the minimum numbers of wavelengths for realizing gossiping in one-hop of optical routing on the ring and the two-dimensional torus of N nodes are cN/sup 2/ and cN/sup 3/2/, c /spl ap/ 1/8, respectively. These numbers can be too large even for moderate values of N. One approach to reduce the number of wavelengths is to realize gossiping in multihops of routing. We give routing algorithms which realize gossiping in k-hops (k /spl ges/ 2) by O(N/sup 1+1/k/) wavelengths on the ring, O(N/sup 1+1/(2k)/) wavelengths on the 2D torus, and O(N/sup 1+1/(3k)/) wavelengths on the 3D torus on a simple multihop routing model. We also discuss the multihop routing for gossiping on a merge model. We give the upper bounds on the numbers of wavelengths for gossiping in two-hops and three-hops for the ring, 2D torus, and 3D torus on the merge model.     

Uniform leader election protocols for radio networks

A radio network is a distributed system with no central arbiter, consisting of n radio transceivers, henceforth referred to as stations. We assume that the stations are identical and cannot be distinguished by serial or manufacturing number. The leader election problem asks to designate one of the stations as leader. In this work, we focus on single-channel, single-hop radio networks. We assume that time is slotted and all transmissions occur at slot boundaries. In each time slot, the stations transmit on the channel with some probability until, eventually, one of the stations is declared leader. A leader election protocol is said to be uniform if, in each time slot, every station transmits with the same probability. In a seminal paper, Willard (1986) presented a uniform leader election protocol for single-channel single-hop radio stations terminating in log log n+o(log log n) expected time slots. It was open for more than 15 years whether Willard's protocol featured the same time performance with "high probability." One of our main contributions is to show that, unfortunately, this is not the case. Specifically, we prove that for every parameter f∈e^O(n), in order to ensure termination with probability exceeding 1-1/f, Willard's protocol must take log log n+Ω(√f) time slots. The highlight of this work is a novel uniform leader election protocol that terminates, with probability exceeding 1-1/f, in log log n+o(log log n)+O(log f) time slots. Finally, we provide simulation results that show that our leader election protocol outperforms Willard's protocol in practice     

Distributed sorting algorithms for multi-channel broadcast networks

A multi-channel broadcast network is a distributed computation model in which p independent processors communicate over a set of p shared broadcast channels. Computation proceeds in synchronous cycles, during each of which the processors first write and read the channels, then perform local computations. Performance is measured in terms of the number of cycles used in the computation, where each bit to be transmitted is assumed to require a separate cycle. In this paper we investigate the problem of sorting p bit strings of uniform length m, each string initially located at a different processor in the broadcast network. We develop an efficient sorting method that first reduces the length of the strings without affecting their relative order, then proceeds using only the shorter strings. A sequence of three successively improved algorithms based on this approach is presented, the best of which runs in O(m + p log p) cycles. By showing a lower bound of Ω(m) cycles, we prove that the algorithm is optimal for sufficiently large m. Our results improve by a factor of log p the solution of the multiple identification problem presented by Landau, Yung and Galil (1985).