Efficient multicast search under delay and bandwidth constraints

The issue of a multicast search for a group of users is discussed in this study. Given the condition that the search is over only after all the users in the group are found, this problem is called the Conference Call Search (CCS) problem. The goal is to design efficient CCS strategies under delay and bandwidth constraints. While the problem of tracking a single user has been addressed by many studies, to the best of our knowledge, this study is one of the first attempts to reduce the search cost for multiple users. Moreover, as oppose to the single user tracking, for which one can always reduce the expected search delay by increasing the expected search cost, for a multicast search the dependency between the delay and the search cost is more complicated, as demonstrated in this study. We identify the key factors affecting the search efficiency, and the dependency between them and the search delay. Our analysis shows that under tight bandwidth constraints, the CCS problem is NP-hard. We therefore propose a search method that is not optimal, but has a low computational complexity. In addition, the proposed strategy yields a low search delay as well as a low search cost. The performance of the proposed search strategy is superior to the implementation of an optimal single user search on a group of users. Amotz Bar-Noy received the B.Sc. degree in 1981 in Mathematics and Computer Science and the Ph.D. degree in 1987 in Computer Science, both from the Hebrew University, Israel. From October 1987 to September 1989 he was a post-doc fellow in Stanford University, California. From October 1989 to August 1996 he was a Research Staff Member with IBM T. J. Watson Research Center, New York. From February 1995 to September 2001 he was an associate Professor with the Electrical Engineering-Systems department of Tel Aviv University, Israel. From September 1999 to December 2001 he was with AT research labs in New Jersey. Since February 2002 he is a Professor with the Computer and Information Science Department of Brooklyn College - CUNY, Brooklyn New York. Zohar Naor received the Ph.D. degree in Computer Science from Tel Aviv University, Tel Aviv, Israel, in 2000. Since 2003 he is with the University of Haifa, Israel. His areas of interests include wireless networks, resource management of computer networks, mobility, search strategies, and multiple access protocols.     

Designing broadcasting algorithms in the postal model for message-passing systems

In many distributed-memory parallel computers and high-speed communication networks, the exact structure of the underlying communication network may be ignored. These systems assume that the network creates a complete communication graph between the processors, in which passing messages is associated with communication latencies. In this paper we explore the impact of communication latencies on the design of broadcasting algorithms for fully connected message-passing systems. For this purpose, we introduce thepostal model that incorporates a communication latency parameter 1. This parameter measures the inverse of the ratio between the time it takes an originator of a message to send the message and the time that passes until the recipient of the message receives it. We present an optimal algorithm for broadcasting one message in systems withn processors and communication latency , the running time of which is (( logn)/log( + 1)). For broadcastingm 1 messages, we first examine several generalizations of the algorithm for broadcasting one message and then analyze a family of broadcasting algorithms based on degree-d trees. All the algorithms described in this paper are practical event-driven algorithms that preserve the order of messages.     

Sensor allocation in diverse environments

Sensor coverage varies with location due to factors such as weather, terrain, and obstacles. If a field can be partitioned into zones of homogeneous sensing areas, then the area covered by a random deployment of sensors can be optimized by controlling the number of sensors deployed in each zone. This paper provides formulas to directly calculate the optimal sensor partition in runtime asymptotically equal to the number of zones; to determine the minimum sensor count required to achieve a specific coverage threshold; and to bound the maximum increase in coverage over a strategy oblivious to differences in sensing areas. Results show that this bound is no greater than 13% for a field with two zones. While the analytical solutions assume that each zone is covered independently, sensors are allowed to affect neighboring zones in simulations. Nevertheless, the simulation results support the optimality of the solutions.     

Nearly optimal perfectly periodic schedules

We consider the problem of scheduling a set of pages on a single broadcast channel using time-multiplexing. In a perfectly periodic schedule, time is divided into equal size slots, and each page is transmitted in a time slot precisely every fixed interval of time (the period of the page). We study the case in which each page i has a given demand probability , and the goal is to design a perfectly periodic schedule that minimizes the average time a random client waits until its page is transmitted. We seek approximate polynomial solutions. Approximation bounds are obtained by comparing the costs of a solution provided by an algorithm and a solution to a relaxed (non-integral) version of the problem. A key quantity in our methodology is a fraction we denote by , that depends on the maximum demand probability: . The best known polynomial algorithm to date guarantees an approximation of . In this paper, we develop a tree-based methodology for perfectly periodic scheduling, and using new techniques, we derive algorithms with better bounds. For small values, our best algorithm guarantees approximation of . On the other hand, we show that the integrality gap between the cost of any perfectly periodic schedule and the cost of the fractional problem is at least . We also provide algorithms with good performance guarantees for large values of . Received: December 2001 / Accepted: September 2002     

Choice coordination with limited failure

The Choice Coordination Problem requiresn asynchronous processes to reach a common choice of one out ofk possible alternatives. Processes communicate viak shared variables. Up tot, t, of the processes may fail to operate by suddenly quitting the protocol. Rabin (1982) presented lower and upper bounds for the extreme caset=n–1. We present deterministic and randomized algorithms for arbitraryt using an alphabet of sizeO(t ²). A semi-synchronous model is also studied. A reduction to a consensus problem proves the necessity to assume some powerful atomic shared-memory operations.     

Broadcasting info-pages to sensors: efficiency versus energy conservation

In sensor networks applied to monitoring applications, individual sensors may perform preassigned or on-demand tasks, or missions. Data updates (info-pages) may be sent to sensors from a command center, via a time-division broadcast channel. Sensors are normally put in sleep mode when not actively listening, in order to conserve energy in their batteries. Hence, a schedule is required that specifies when sensors should listen for updates and when they should sleep. The performance of such a schedule is evaluated based on data-related costs and sensor-related costs. Data-related costs reflect the obsoleteness of current sensor data, or the delay while sensors wait for updated instructions. Sensor-related costs reflect the energy that sensors consume while accessing the broadcast channel and while switching between the active and sleeping modes (rebooting). Our goal is a schedule with the minimum total cost. Previous related work has explored data-related costs, but listening cost has been addressed only under the assumption that the rebooting operation is free. This paper formulates a new cost model, which recognizes the cost of sensor rebooting. We derive an optimal schedule for the single-sensor setting. We proceed to consider schedules of multiple sensors; we formulate a mathematical program to find an optimal fractional schedule for this setting and provide a solution to the lower bound. Several heuristics for scheduling multiple sensors are introduced and analyzed, and various tradeoffs among the cost factors are demonstrated.     

Shifting gears: Changing algorithms on the fly to expedite Byzantine agreement

We describe several new algorithms for Byzantine agreement. The first of these is a simplification of the original exponential-time Byzantine agreement algorithm due to Pease, Shostak, and Lamport, and is of comparable complexity to their algorithm. However, its proof is very intuitively appealing. A technique of shifting between algorithms for solving the Byzantine agreement problem is then studied. We present two families of algorithms obtained by applying a shift operator to our first algorithm. These families obtain the same rounds to message length trade-off as do Coan's families but do not require the exponential local computation time (and space) of his algorithms. We also describe a modification of an -resilient algorithm for Byzantine agreement of Dolev, Reischuk, and Strong. Finally, we obtain a hybrid algorithm that dominates all our others, by beginning execution of an algorithm in one family, first shifting into an algorithm of the second family, and finally shifting into an execution of the adaptation of the Dolev, Reischuk, and Strong algorithm.     

Broadcasting in multi-radio multi-channel wireless networks using simplicial complexes

We consider the broadcasting problem in multi-radio multi-channel ad hoc networks. The objective is to minimize the total cost of the network-wide broadcast, where the cost can be of any form that is summable over all the transmissions (e.g., the transmission and reception energy, the price for accessing a specific channel). Our technical approach is based on a simplicial complex model that allows us to capture the broadcast nature of the wireless medium and the heterogeneity across radios and channels. Specifically, we show that broadcasting in multi-radio multi-channel ad hoc networks can be formulated as a minimum spanning problem in simplicial complexes. We establish the NP-completeness of the minimum spanning problem and propose two approximation algorithms with order-optimal performance guarantee. The first approximation algorithm converts the minimum spanning problem in simplical complexes to a minimum connected set cover (MCSC) problem. The second algorithm converts it to a node-weighted Steiner tree problem under the classic graph model. These two algorithms offer tradeoffs between performance and time-complexity. In a broader context, this work appears to be the first that studies the minimum spanning problem in simplicial complexes and weighted MCSC problem.     

Decision-driven scheduling

Real-Time Systems - This paper presents a scheduling model, called decision-driven scheduling, elaborates key optimality results for a fundamental scheduling model, and evaluates new heuristics...     

A partial equivalence between shared-memory and message-passing in an asynchronous fail-stop distributed environment

This paper presents a schematic algorithm for distributed systems. This schematic algorithm uses a black-box procedure for communication, the output of which must meet two requirements: a global-order requirement and a deadlock-free requirement. This algorithm is valid in any distributed system model that can provide such a communication procedure that complies with these requirements. Two such models exist in an asynchronous fail-stop environment: one in the shared-memory model and one in the message-passing model. The implementation of the block-box procedure in these models enables us to translate existing algorithms between the two models whenever these algorithms are based on the schematic algorithm.We demonstrate this idea in two ways. First, we present a randomized algorithm for the consensus problem in the message-passing model based on the algorithm of Aspnes and Herlihy [AH] in the shared-memory model. This solution is the fastest known randomized algorithm that solves the consensus problem against a strong fail-stop adversary with one-half resiliency. Second, we solve the processor renaming problem in the shared-memory model based on the solution of Attiyaet al. [ABD⁺] in the message-passing model. The existence of the solution to the renaming problem should be contrasted with the impossibility result for the consensus problem in the shared-memory model [CIL], [DDS], [LA].A preliminary version of this paper, Shared-Memory vs. Message-Passing in an Asynchronous Distributed Environment, appeared inProc. 8th ACM Symp. on Principles of Distributed Computing, pp. 307–318, 1989. Part of this work was done while A. Bar-Noy visited the Computer Science Department, Stanford University, Stanford, CA 94305, USA, and his research was supported in part by a Weizmann fellowship, by Contract ONR N00014-88-K-0166, and by a grant of Stanford's Center for Integrated Systems.