Broadcast Problem Research Articles

Cooperative Multihop Broadcast for Wireless Networks

We address the minimum-energy broadcast problem under the assumption that nodes beyond the nominal range of a transmitter can collect the energy of unreliably received overheard signals. As a message is forwarded through the network, a node will have multiple opportunities to reliably receive the message by collecting energy during each retransmission. We refer to this cooperative strategy as accumulative broadcast. We seek to employ accumulative broadcast in a large scale loosely synchronized, low-power network. Therefore, we focus on distributed network layer approaches for accumulative broadcast in which loosely synchronized nodes use only local information. To further simplify the system architecture, we assume that nodes forward only reliably decoded messages. Under these assumptions, we formulate the minimum-energy accumulative broadcast problem. We present a solution employing two subproblems. First, we identify the ordering in which nodes should transmit. Second, we determine the optimum power levels for that ordering. While the second subproblem can be solved by means of linear programming, the ordering subproblem is found to be NP-complete. We devise a heuristic algorithm to find a good ordering. Simulation results show the performance of the algorithm to be close to optimum and a significant improvement over the well known BIP algorithm for constructing energy-efficient broadcast trees. We then formulate a distributed version of the accumulative broadcast algorithm that uses only local information at the nodes and has performance close to its centralized counterpart.

Multiuser Transmit Optimization for Multicarrier Broadcast Channels: Asymptotic FDMA Capacity Region and Algorithms

We derive optimal and suboptimal multiuser transmit-optimization methods for a multicarrier broadcast channel with intersymbol interference under the frequency-division multiple-access (FDMA) restriction. The general FDMA-based multicarrier broadcast problem is formulated as a maximum weighted rate-sum problem. Given each user's subchannel assignment, the optimal transmit strategy is achieved by multilevel waterfilling. Unfortunately, the problem of finding the optimal subchannel assignments is combinatorial. However, by relaxing the FDMA restriction, we obtain a convex reformulation that allows for efficient computation of the optimal solution, and therefore, a characterization of the FDMA capacity region for a broadcast channel. If all users share the same transmission medium, we prove that the optimal frequency partitioning among the users has an ordered structure that can be exploited to significantly reduce the computational complexity. To make multiuser transmit-optimization schemes practical for applications with relatively fast time-varying user data-rate requirements or priorities, further reduction in computational complexity is necessary. This is achieved by restricting the energy distribution to be constant across the used subchannels. Simulations indicate the low-complexity constant-energy methods presented are very robust, and suffer from negligible performance loss.

Logarithmic inapproximability of the radio broadcast problem

We show that the radio broadcast problem is Ω( logn) -inapproximable unless NP⊆BPTIME( n O(loglog n) ). This is the first result on the hardness of approximation of this problem. Our reduction is based on the reduction from the Label-Cover problem to the Set Cover problem due to Lund and Yannakakis [J. Assoc. Comput. Mach. 41 (5) (1994) 960–981], and uses some new ideas.

Atomic broadcast in asynchronous crash-recovery distributed systems and its use in quorum-based replication

Atomic broadcast is a fundamental problem of distributed systems: It states that messages must be delivered in the same order to their destination processes. This paper describes a solution to this problem in asynchronous distributed systems in which processes can crash and recover. A consensus-based solution to atomic broadcast problem has been designed by Chandra and Toueg for asynchronous distributed systems where crashed processes do not recover. We extend this approach: it transforms any consensus protocol suited to the crash-recovery model into an atomic broadcast protocol suited to the same model. We show that atomic broadcast can be implemented requiring few additional log operations in excess of those required by the consensus. The paper also discusses how additional log operations can improve the protocol in terms of faster recovery and better throughput. To illustrate the use of the protocol, the paper also describes a solution to the replica management problem in asynchronous distributed systems in which processes can crash and recover. The proposed technique makes a bridge between established results on weighted voting and recent results on the consensus problem.

The Data Broadcast Problem with Non-Uniform Transmission Times

The Data Broadcast Problem consists of finding an infinite schedule to broadcast a given set of messages so as to minimize a linear combination of the average service time to clients requesting messages, and of the cost of the broadcast. This problem also models the Maintenance Scheduling Problem and the Multi-Item Replenishment Problem. Previous work concentrated on a discrete-time restriction where all messages have transmission time equal to 1. Here, we study a generalization of the model to a setting of continuous time and messages of non-uniform transmission times. We prove that the Data Broadcast Problem is strongly NP -hard, even if the broadcast costs are all zero, and give 3-approximation algorithms.

Broadcast in point-point network with quantum mechanism

A method for solving the broadcast problem in a point–point network with 1/3 players being a false player is presented. The method explores the interesting property of Qutrits (quantum triplets) in the Aharonov State and solves the broadcast problem at the price of sharing the Qutrits among the players in the initial phase.

Solving the group priority inversion problem in a timed asynchronous system

Considers the priority inversion problem in an actively replicated system. Priority inversion was originally defined in the context of nonreplicated systems. Therefore, we first introduce the concept of group priority inversion, which extends the concept of (local) priority inversion to the context of a group of processors that perform an actively replicated processing. We then present the properties of a request scheduling protocol to enforce a total ordering for the processing of requests while avoiding group priority inversions. These properties have been implemented in a protocol that relies on a timed asynchronous system model equipped with a failure detector of the class /spl diams/S. The proposed solution allows us to replicate a critical server while ensuring that the processing of all the incoming requests is consistent (mechanisms for solving the atomic broadcast problem) and predictable (mechanisms for solving the group priority inversion problem). Thus, the described request scheduling protocol is a key component which can be used to develop fault-tolerant real-time applications in a timed asynchronous system.

Polynomial-Time Algorithms for Minimum-Time Broadcast in Trees

This paper addresses the minimum-time broadcast problem under several modes of the line model, i.e., when long-distance calls can be placed along paths in the network. It is well known that the minimum-time broadcast problem can be solved in polynomial time under the single-port edge-disjoint paths mode. However, it is equally well known that either relaxing the model to the all-port edge-disjoint paths mode, or constraining the model to the single-port vertex-disjoint paths mode, leads to NP-complete problems; and exact solutions have been derived for specific topologies only (e.g., hypercubes or tori). In this paper we present polynomial-time algorithms for minimum-time broadcast in trees. These algorithms are obtained by application of an original technique called the merging method , which can be applied in a larger context, for instance, to solve the multicast problem or to address the restricted regimen. The merging method requires solving the minimal contention-free matrix problem whose solution presents some interest on its own.

Handling message semantics with Generic Broadcast protocols

Message ordering is a fundamental abstraction in distributed systems. However, ordering guarantees are usually purely “syntactic,” that is, message “semantics” is not taken into consideration despite the fact that in several cases semantic information about messages could be exploited to avoid ordering messages unnecessarily. In this paper we define the Generic Broadcast problem, which orders messages only if needed, based on the semantics of the messages. The semantic information about messages is introduced by conflict relations. We show that Reliable Broadcast and Atomic Broadcast are special instances of Generic Broadcast. The paper also presents two algorithms that solve Generic Broadcast.

Optimally balanced spanning tree of the star network

The one-to-all personalized broadcast problem in an interconnection network can be optimally solved with respect to both the time and the number of transmissions if it is possible to construct an optimally balanced spanning tree of the network which is also a shortest path tree. We give an algorithm to construct an optimally balanced spanning tree of the star network which is also a shortest path tree. Our result is optimal and improves on that of Chen et al. (1996) and Day and Tripathi (1994).

A case study in the mechanical verification of fault tolerance

To date, there is little evidence that modular reasoning about fault-tolerant systems can simplify the verification process in practice. This question is studied using a prominent example from the fault tolerance literature: the problem of reliable broadcast in point-to-point networks subject to crash failures of processes. The experiences from this case study show how modular specification techniques and rigorous proof re-use can indeed help in such undertakings.

On the structure of minimum broadcast digraphs

Broadcasting is a problem of information dissemination described for a group of individuals connected by a communication network, where one individual has an item of information and needs to communicate it to everyone else. Numerous previous papers have investigated ways to construct sparse undirected graphs (networks) in which this process can be completed in minimum time. In this paper, we consider the broadcast problem in directed graphs. We describe and recall some techniques to construct sparse digraphs on n vertices in which broadcasting can be completed in minimum time. For n=2 p−1 and n=2 p−2 , we show that these techniques produce the sparsest possible digraphs of this type (called minimum broadcast digraphs, or MBDs). In the case n=2 p−1 , we give one class of MBDs, as for the case n=2 p−2 , we give two non isomorphic classes of MBDs. We also show a class of MBDs on n=2 p vertices which is non isomorphic to the one given in Liestman and Peters (Discrete Appl. Math. 37/38 (1992) 401–419). For some other infinite classes of values of n ( n=2 p−1+1, n=2 p−3 and n=2 p−4 ), we also give techniques that produce the best lower and upper bounds on the size of MBDs known so far.

On Indexed Data Broadcast

We consider the problem of efficient information retrieval in asymmetric communication environments where multiple clients with limited resources retrieve information from a powerful server who periodically broadcasts its information repository over a communication medium. The cost of a retrieving client consists of two components: (a) access time, defined as the total amount of time spent by a client in retrieving the information of interest, and (b) tuning time, defined as the time spent by the client in actively listening to the communication medium, measuring a certain efficiency in resource usage. A probability distribution is associated with the data items in the broadcast, representing the likelihood of a data item's being requested at any point of time. The problem of indexed data broadcast is to schedule the data items interleaved with certain indexing information in the broadcast so as to minimize simultaneously the mean access time and the mean tuning time. Prior work on this problem thus far has focused only on some special cases. In this paper we study the indexed data broadcast problem in its full generality and design a broadcast scheme that achieves a mean access time of at most (1.5+ε) times the optimal and a mean tuning time bounded by O(logn).

On the All-to-All Broadcast Problem in Optical Networks 1

This paper considers the transmission of uniform deterministic traffic in an optical broadcast-star network using Wavelength Division Multiplexing. Lower bounds are established on the minimum time to exchange information between every node pair in such a network with tunable transmitters and fixed-tuned receivers. Three different scheduling algorithms are developed that are strictly optimal in three regimes of system parameters. The results are applicable to arbitrary tuning delays and arbitrary numbers of wavelength channels, and indicate the existence of a well-defined transition regime from tuning-limited operation to bandwidth-limited operation. Finally, the problem of computing the optimal number of wavelengths is addressed to achieve a schedule with minimum schedule length, and exact solutions are given.

Neighbourhood information dissemination in the star graph

This paper studies two neighborhood information dissemination problems in the star graph (n-star): The neighborhood broadcast problem (NBP) is the problem of disseminating a message from the source vertex to all the vertices adjacent to the source vertex and the neighborhood gossiping problem (NGP) is the problem of exchanging messages among all neighboring vertices in the given graph. We propose two neighborhood information dissemination schemes in n-star under the single-port, half-duplex model: The first scheme completes a neighborhood broadcast in 1.5 log/sub 2/ n+O(1) time units and the second scheme completes a neighborhood gossiping in 2.88 log/sub 2/ n+o(logn) time units. We also derive a lower bound on the neighborhood gossiping of 2.88 log/sub 2/ n+O(1) time units, which implies that the latter scheme is optimal with respect to the leading term.

Source-limited inclusive routing: A new paradigm for multicast communication

In this paper, we study a combination of the multicast communication problem and the maximum disjoint paths problem. Specifically, we are given a directed tree T rooted at r, and we want to send a message from r to a subset of nodes in T. We accomplish this via a multicast schedule which consists of a number of time steps in which informed nodes deliver the message to uninformed nodes until all destinations have received the message. In each time step, any informed node s may forward the message to one of its uninformed descendant nodes d via the unique directed path, or dipath, p from s to d in ditree T. A multicast schedule is called edge-disjoint if the dipaths used in any time step do not share any edges. We call a multicast schedule a node-disjoint schedule if the dipaths used in any time step are node-disjoint. We show that directed trees can be used to represent source-limited inclusive routing, a realistic class of routing schemes used in popular direct network systems. We then show that node-disjoint multicast schedules in directed trees can be used to closely approximate optimal edge-disjoint multicast schedules. In addition, we show that node-disjoint multicast in directed trees can be reduced to an equivalent broadcast problem in directed trees. We describe an O(n2) greedy algorithm (GA) for performing node-disjoint broadcast in directed trees. The greatest advantages of the GA algorithm are its simplicity and its optimal performance in popular topologies such as meshes, tori, and hypercubes. We also describe an O(n3) algorithm that always produces minimum-length node-disjoint broadcast schedules for directed tree topologies, which can be easily transformed into an algorithm that produces edge-disjoint multicast schedules that are no more than twice the length of an optimal edge-disjoint multicast schedule for an arbitrary topology. © 2000 John Wiley & Sons, Inc.

Scheduling in broadcast networks

Broadcasting in a communications network has been the subject of many studies in recent years. The studies vary in their assumptions governing the behavior of the network and in their objectives with respect to the network. Almost all the work to date uses the unit transmission time assumption, that is, the message transmission times between all pairs of vertices are equal. In this paper, we investigated the broadcast problem under four more general transmission time assumptions. In addition, four different objective functions were considered, including the minimization of (1) the broadcast time (the maximum time for any vertex to receive the message), (2) the average time to receive the message (both with and without ready times at the vertices), (3) the weighted average time to receive the message, and (4) the cycle time. Of the 20 problems thus generated, four admit polynomial time algorithms, 15 are (in the equivalent recognition version) unary NP-complete, and the complexity status of one remains open. All these results are proved, and heuristics with an attainable constant worst-case performance ratio are provided for two of the problems for which polynomial time algorithms are not found. © 1998 John Wiley & Sons, Inc. Networks 32:233–253, 1998

All-to-all broadcast and matrix multiplication in faulty SIMD hypercubes

In this paper, we develop algorithms in order of efficiency for all-to-all broadcast problem in an N=2/sup n/-node n-dimensional faulty SIMD hypercube, Q/sub n/, with up to n-1 node faults. The algorithms use a property of a certain ordering of dimensions. Our analysis includes startup time (/spl alpha/) and transfer time (/spl beta/). We have established the lower bound for such an algorithm to be n/spl alpha/+(2N-3)L/spl beta/ in a faulty hypercube with at most n-1 faults (each node has a value of L bytes). Our best algorithm requires 2n/spl alpha/+2NL/spl beta/ and is near-optimal. We develop an optimal algorithm for matrix multiplication in a faulty hypercube using all-to-all broadcast and compare the efficiency of all-to-all broadcast approach with broadcast approach and global sum approach for matrix multiplication. The algorithms are congestion-free and applicable in the context of available hypercube machines.

Reliable broadcasting in product networks

We investigate the reliability of broadcasting in product networks containing faulty nodes and/or links. Faults considered in this paper are mainly of the Byzantine type, i.e., a faulty node or a faulty link may not only stop sending a message but also arbitrarily change a message passing through the faulty place or even fabricate a false message. We assume that no nodes have a priori information about faults in a network. Hence, the key problem of reliable broadcasting in our model is how to control the message transmission so that any corrupted message cannot affect the result of the broadcasting too much. We propose the concept of an n-channel graph which has n-independent spanning trees rooted at each node. The fault tolerance can be achieved by sending n copies of the message along the n-independent spanning trees rooted at the source node. In this paper we show how to construct n-independent spanning trees of a product network from spanning trees of n-component graphs. Furthermore, we can design an efficient and reliable broadcasting scheme based on independent spanning trees for a product network from simple broadcasting schemes for component networks. The degrees of fault tolerance against crash faults and Byzantine faults of nodes and/or links are, respectively, n − 1 and ⌊( n − 1)/2⌋ in the worst case. We can successfully broadcast with a probability higher than 1 − k −⌈ n 2 ⌉ in any product network of order N consisting of n-component graphs of order b or less, if at most N/4 b 3 nk faulty nodes are randomly distributed in the network. We can also successfully broadcast with a probability higher than 1 − k −⌈ n 2 ⌉ in any product network of size L, of n component graphs of size b or less, if at most L l2b 2 k faulty links are randomly distributed in the network.

On the impact of sense of direction on message complexity

In this paper, we prove a general result on the impact of sense of direction. We show that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast, Depth First Traversal, Election, and Spanning Tree Construction. In systems with n nodes and e communication links, the solution for the Depth First Traversal and the Broadcast problems require Ω(e) messages with arbitrary labelings; we show that, with any sense of direction, they can be solved exchanging only Θ( n) messages, even if the system is anonymous. The problems of Election and of Spanning Tree Construction require Ω(e + n log n) messages with arbitrary labelings; on the other hand, we show that they can be solved with Θ( n) messages with any sense of direction. The results presented here completely explain and generalize the existing results which now follow as corollaries for specific labelings.