Minimum Broadcast Research Articles

Tighter bounds on the minimum broadcast time

Given a connected graph and a subset of its vertices referred to as the sources, the minimum broadcast time problem asks for the shortest time necessary for communicating a message from the sources to all other vertices in the graph. Information exchange is possible only between neighbors, and each vertex can transmit the message to at most one neighbor at a time. Since early works on complexity theory, the problem has been known to be NP-hard. Contributions from the current text to the understanding of the minimum broadcast time problem are threefold. Through considerations of the shortest distances between sources and other vertices, a new lower bound on the broadcast time is derived. Analytical expressions of this bound are given in the single source instances of several graph classes. Fast procedures for computing upper bounds are studied next, including both the construction of feasible solutions, and the improvement of existing ones. Finally, with a focus on a new stable-set interpretation of the problem, integer programming formulations are studied, and for their theoretical interest, associated facet-defining valid inequalities are given. The computational performance of the novel methodology is evaluated in numerical experiments applied to standard benchmark instances and to instances larger than those studied in preceding recent works.

Embedding Knödel Graph into Cube-like Architectures: Dilation Optimization and Wirelength Analysis

An important tool for the execution of parallel algorithms and the simulation of interconnection networks is graph embedding. The quality of an embedding can be assessed using some cost metrics. The dilation and wirelength are the commonly used parameters. The Knödel graph [Formula: see text] is a minimum linear gossip network and has minimum broadcasting. It has [Formula: see text] vertices, [Formula: see text] edges, where [Formula: see text] is even, and [Formula: see text]log[Formula: see text]. In this study, we solve the dilation problem of embedding the Knödel graph into certain cube-like architectures such as hypercube, folded hypercube, and augmented cube. In [G. Fertin, A. Raspaud, A survey on Knödel graphs, Discrete Applied Mathematics 137 (2004) 173–195], it is proved that the dilation of embedding the Knödel graph [Formula: see text] into the hypercube [Formula: see text] is at most [Formula: see text]. In this study, we obtain an improved upper bound for dilation of embedding the Knödel graph into the hypercube and it is equal to [Formula: see text]. Also, we calculate the wirelength of embedding the Knödel graph into the above-said cube-like architectures using dilation.

Strong bounds and exact solutions to the minimum broadcast time problem

AbstractGiven a graph and a subset of its nodes, referred to as source nodes, the minimum broadcast time problem asks for the minimum number of steps in which a signal can be transmitted from the sources to all other nodes in the graph. In each step, the sources and the nodes that already have received the signal can forward it to at most one of their neighbour nodes. The problem has previously been proved to be NP‐hard. In the current work, we develop a compact integer programming model for the problem. We also devise procedures for computing lower bounds on the minimum number of steps required, along with methods for constructing near‐optimal solutions. Computational experiments demonstrate that in a wide range of instances, in particular instances with sufficiently dense graphs, the lower and upper bounds under study collapse. In instances where this is not the case, the integer programming model proves strong capabilities in closing the remaining gap and proves to be considerably more efficient than previously studied models.

Optimal Broadcasting in Fully Connected Trees

Broadcasting is disseminating information in a network where a specific message must spread to all network vertices as quickly as possible. Finding the minimum broadcast time of a vertex in an arbitrary network is proven to be NP-complete. However, this problem is solvable for a few families of networks. In this paper, we present an optimal algorithm for finding the broadcast time of any vertex in a fully connected tree ([Formula: see text]) in [Formula: see text] time. An [Formula: see text] is formed by attaching arbitrary trees to vertices of a complete graph of size [Formula: see text] where [Formula: see text] is the total number of vertices in the graph.

A matheuristic approach for the minimum broadcast time problem using a biased random‐key genetic algorithm

AbstractThe Minimum Broadcast Time (MBT) is a well‐known data dissemination problem whose goal is to find a broadcast scheme that minimizes the number of steps needed to execute the broadcast operation. The problem has many applications in distributed systems and, in particular, the Industry 4.0 domain. Because Industry 4.0 applications rely primarily on the use of large‐scale machine to machine communications, they need data dissemination techniques that combine high reliability with low communication latency. This work proposes a Biased Random‐Key Genetic Algorithm and a matheuristic for the MBT. We carry out experiments with our algorithms on instances commonly used in the literature (hypercube, shuffle exchange, cube‐connected cycles, de Bruijn, Harary graphs), and also on massive synthetic instances (up to 1000 vertices), allowing to cover many possibilities of real industry topologies. Our proposal is also compared with state‐of‐the‐art exact methods and heuristics. Experimental results show that our algorithm is able to outperform the best‐known heuristics for the MBT, and also that it is a very good alternative for large instances that cannot be solved by current exact methods.

A tree-block decomposition-based heuristic for the minimum broadcast time

The problem under study is the minimum broadcast time. Given an undirected connected graph and a singleton that owns a message, the goal is to broadcast this message as soon as possible, where the communication takes place between neighbouring-nodes in a selective fashion and each forwarding takes one time-slot. Historically, this problem finds applications in telephonic services; however, it serves as an inspirational problem for the design of current delay-tolerant forwarding schemes in modern communication systems like content delivery networks and peer-to-peer networks. The problem belongs to the NP-complete class. As a consequence, the literature offers heuristics, approximation algorithms and exact exponential-time solutions. The contributions of this paper are two-fold. First, an efficient integer linear programming formulation for the problem is provided. Second, a competitive heuristic called TreeBlock, is developed. A fair comparison between TreeBlock and previous heuristics highlights the effectiveness of our proposal.

A tree-block decomposition-based heuristic for the minimum broadcast time

The problem under study is the minimum broadcast time. Given an undirected connected graph and a singleton that owns a message, the goal is to broadcast this message as soon as possible, where the communication takes place between neighbouring-nodes in a selective fashion and each forwarding takes one time-slot. Historically, this problem finds applications in telephonic services; however, it serves as an inspirational problem for the design of current delay-tolerant forwarding schemes in modern communication systems like content delivery networks and peer-to-peer networks. The problem belongs to the NP-complete class. As a consequence, the literature offers heuristics, approximation algorithms and exact exponential-time solutions. The contributions of this paper are two-fold. First, an efficient integer linear programming formulation for the problem is provided. Second, a competitive heuristic called TreeBlock, is developed. A fair comparison between TreeBlock and previous heuristics highlights the effectiveness of our proposal.

TDSM: Trusted Dissemination Safety Messages in a Multi-hop V2V Communication

Broadcasting is a transmission of the same message to multiple recipients to form the communication process between wireless vehicular networks. Yet, many challenges still need to be addressed to ensure proper broadcasting. These include resolving the different security problems that affect the vehicular network efficiency while exchanging messages, and achieving low dissemination overhead and minimum broadcast delay while maintaining high delivery ratio. In this paper, we present a novel model for trusting the safety message before disseminating it, through multi-hop V2V communication. We also, ensured message high delivery rate with minimum time delay. To this end, we recommend the idea of dividing the digital roadmap of the interested area into small fixed size segments. To transmit the packets between vehicles, we depend on pairs of concatenated information composed of the beacon message and the safety message, where the sending time is arranged according to the road density. The model relies on the idea of using a forwarder to rebroadcast the safety message between segments. Choosing the best forwarder is thus based on a calculated weight value for links between the vehicles. Our contribution is achieved by adding two decentralized data trust stages: to entrust the safety message information in one-hop, and before disseminating it farther through multi-hop. The simulation results using NS2 and SUMO showed the effectiveness of the model. The two stages of the trust method are also verified.

$\Sigma$ -Scan: A Mobile Beacon-Assisted Localization Path-Planning Algorithm for Wireless Sensor Networks

Deploying static beacons to help sensor localization is a common approach in wireless sensor network. Alternatively, adopting a mobile beacon to travel along a specific trajectory and to broadcast its locations at specific points is more efficient. Therefore, path planning of the mobile beacon originally focused on finding shortest path length and minimum broadcast points, such as Scan and Hilbert, to decrease power consumption. More recently, path planning increasingly attempted to achieve higher accuracy, such as Double-scan and Z-scan. However, optimal trade-off between power efficiency and localization accuracy is yet to be achieved. In this paper, we designed $\Sigma $ -Scan which aims to reach high accuracy and coverage with short path length by combining the advantages of Scan and Z-scan. $\Sigma $ -Scan provides three kinds of unit to constitute arbitrary rectangles and minimize the minimum bounding rectangle. Compared to them, $\Sigma $ -Scan is more applicable, accessible and easy to implement. The simulation results show that compared to other previous approaches, $\Sigma $ -Scan has the highest ratio of accuracy and coverage to path length and also decreases the incidence of collinearity in time-priority trilateration (TPT).

A new construction of broadcast graphs

Given a graph G=(V,E) and an originator vertex v, broadcasting is an information disseminating process of transmitting a message from the vertex v to all vertices of the graph G as quickly as possible. A graph G on n vertices is called broadcast graph if the broadcasting from any vertex in the graph can be accomplished in ⌈logn⌉ time. A broadcast graph with the minimum number of edges is called minimum broadcast graph. The number of edges in a minimum broadcast graph on n vertices is denoted by B(n). A long sequence of papers present different broadcast graph constructions and upper bounds on B(n). In this paper, we improve the compounding method and construct new broadcast graphs with a better upper bound on B(n). Consequently, we show that B(n)≤(m−k+1)n−(2m−k+1−2)(m−2q+1)2q−1 for n∈[2m−1+1,2m−2m2+1], where n=2m−2k−d, m≥5, 2≤k≤m−2, 0≤d≤2k−1, and q=min(⌊m−22⌋,k−2).

Heuristics for the Minimum Broadcast Time

The problem under study is the Minimum Broadcast Time (MBT). We are given a simple graph and a singleton that owns a message. The goal is to disseminate the message as soon as possible, where the communication takes place between neighboring-nodes in a selective fashion and each forwarding takes one time-slot. The MBT serves as an inspirational problem for the design of delay-sensitive forwarding schemes. Since the problem belongs to the NP-Hard class, the literature offers heuristics, approximation algorithms and exact exponential-time solutions.The contributions of this paper are two-fold. First, an ILP formulation for the problem is provided. Second, a competitive heuristic is developed. A fair comparison between TreeBlock and previous heuristics highlights the effectiveness of our proposal.

Minimum multiple originator broadcast graphs

Broadcasting from multiple originators is a variant of broadcasting in which any k vertices may be the originators of a message in a network of n vertices. A minimum broadcast graph has the fewest possible edges while still allowing minimum time broadcasting from any set of k originators. We provide a census of all known such graphs.

Shortest Path Minimum Broadcast Energy Conserving Protocol for Asymmetric WSN

Wireless sensor network is dynamic in nature and completely operates on infrastructure less environment. It discovers routes dynamically to reach the destination. Securing a dynamic route which is not known before communication is always a challenge. Energy conservation and finding the shortest path is a key challenge. In this paper propose a shortest path Minimum Broadcast Energy conserving (SME) Protocol for Asymmetric Wireless Sensor Network. It finds the shortest path in minimum broadcasts and conserves energy in asymmetric wireless network. The basic idea behind SME is to improve upon RP, Layhet, Egyhet from the state of the art and achieve performance enhancement with better delivery rate consuming minimum energy and slow sinking with reduction in energy during data routing process for data transmission to destination for the route selected in an asymmetric environment. Asymmetric indicates where two end nodes may not use the same path to communicate with each other. KeywordsWireless Sensor Network, RP, Layhet, Egyhet, SME.

On Minimum-Latency Broadcast in Multichannel Duty-Cycled Wireless Sensor Networks

Broadcast has critical significance for wide application of wireless sensor networks (WSNs). Minimum-latency broadcast (MLB) studies how to devise a broadcast schedule, which can achieve minimum broadcast latency with no signal interference. In multichannel duty-cycled WSNs, nodes can exploit multiple channels to communicate and periodically fall asleep after working for some time. Nevertheless, most solutions to the MLB problem either focus on nonsleeping scenarios or only exploit one single channel. Therefore, we investigate the MLB problem in multichannel duty-cycled WSNs in this paper and call this problem as MLBCD problem. We prove that MLBCD problem is NP-hard. We propose a new concept of active interference graph (AIG). Based on AIG, we present one novel approximation broadcast algorithm called NAB to solve the MLBCD problem. We prove that our proposed NAB algorithm achieves provable performance guarantee. The results of our extensive evaluations show that NAB algorithm can significantly improve the broadcast latency.

Minimum Latency Broadcast in the SINR Model: A Parallel Routing and Scheduling Approach

We study the minimum latency data broadcast problem under the signal-to-interference-plus-noise-ratio (SINR) model, which is known to capture wireless interference more accurately and realistically than the widely used graph-based models. Previous work mainly involves building a broadcast tree first and then computing interference-aware TDMA schedules for the links on the tree. Observing that the separation of routing and scheduling may lead to unsaturated transmissions in each time slot, we develop a polynomial-time heuristic algorithm, namely PRS, by advocating a parallel way of constructing routing and transmission schedules. Theoretical analysis indicates that PRS generates correct schedules under the SINR constraints. Simulation results demonstrate that PRS outperforms state-of-the-art algorithms in terms of broadcast latency under various network conditions.

Efficient construction of broadcast graphs

A broadcast graph is a connected graph, G=(V,E), |V|=n, in which each vertex can complete broadcasting of one message within at most t=⌈logn⌉ time units. A minimum broadcast graph on n vertices is a broadcast graph with the minimum number of edges over all broadcast graphs on n vertices. The cardinality of the edge set of such a graph is denoted by B(n). In this paper we construct a new broadcast graph with B(n)≤(k+1)N−(t−k2+2)2k+t−k+2, for n=N=(2k−1)2t+1−k and B(n)≤(k+1−p)n−(t−k2+p+2)2k+t−k−(p−2)2p, for 2t<n<(2k−1)2t+1−k, where t≥7, 2≤k≤⌊t/2⌋−1 for even n and 2≤k≤⌈t/2⌉−1 for odd n, d=N−n, x=⌊d2t+1−k⌋ and p=⌊log2(x+1)⌋ if x>0 and p=0 if x=0.The new bound is an improvement upon the bounds appeared in Bermond et al. (1995), Bermond et al. (1997), Fertin and Raspaud (2004) and Harutyunyan and Leistman (1999) and the recent bound presented by Harutyunyan and Liestman (2012) for odd values of n.

Minimum Broadcasting Structure for Optimal Data Dissemination in Vehicular Networks

In this paper, we model a vehicular multihop network as an evolving graph and formulate the problem of optimal data dissemination over the network in terms of minimum number of transmissions. We show that the problem belongs to the NP complexity class and provide an easy to implement polynomial-time 2 τH(Δ)-approximation algorithm, where τ is the number of different subgraphs that comprise the evolving graph, and H(Δ) is the harmonic number of the degree of the evolving graph. By means of applying our heuristic over a vehicular scenario generated by a microscopic road-traffic simulator, we provide some insight into the data dissemination issue. In addition, the proposed algorithm is employed to benchmark a state-of-the-art communication protocol. We hope this paper will inspire more efficient heuristics and data dissemination solutions.

Routing and transmission scheduling for minimizing broadcast delay in multirate wireless mesh networks using directional antennas

Using directional antennas to reduce interference and improve throughput in multihop wireless networks has attracted much attention from the research community in recent years. In this paper, we consider the issue of minimum delay broadcast in multirate wireless mesh networks using directional antennas. We are given a set of mesh routers equipped with directional antennas, one of which is the gateway node and the source of the broadcast. Our objective is to minimize the total transmission delay for all the other nodes to receive a broadcast packet from the source, by determining the set of relay nodes and computing the number and orientations of beams formed by each relay node. We propose a heuristic solution with two steps. Firstly, we construct a broadcast routing tree by defining a new routing metric to select the relay nodes and compute the optimal antenna beams for each relay node. Then, we use a greedy method to make scheduling of concurrent transmissions without causing beam interference. Extensive simulations have demonstrated that our proposed method can reduce the broadcast delay significantly compared with the methods using omnidirectional antennas and single-rate transmission. In addition, the results also show that our method performs better than the method with fixed antenna beams. Copyright © 2012 John Wiley & Sons, Ltd.

Upper bounds on the broadcast function using minimum dominating sets

We construct new upper bounds on the broadcast function B(n), the number of edges in a minimum broadcast graph on n vertices, for a large class of integers n. The bounds are obtained by a construction that uses the minimum size of dominating sets for some Knödel graphs. We also determine the domatic number of these graphs.

A decomposition approach for solving a broadcast domination network design problem

We consider an optimization problem that integrates network design and broadcast domination decisions. Given an undirected graph, a feasible broadcast domination is a set of nonnegative integer powers fi assigned to each node i, such that for any node j in the graph, there exists some node k having a positive fk-value whose shortest distance to node j is no more than fk. The cost of a broadcast domination solution is the sum of all node power values. The network design problem constructs edges that decrease the minimum broadcast domination cost on the graph. The overall problem we consider minimizes the sum of edge construction costs and broadcast domination costs. We show that this problem is NP-hard in the strong sense, even on unweighted graphs. We then propose a decomposition strategy, which iteratively adds valid inequalities based on optimal broadcast domination solutions corresponding to the first-stage network design solutions. We demonstrate that our decomposition approach is computationally far superior to the solution of a single large-scale mixed-integer programming formulation.