Binary linear programming models for robust broadcasting in communication networks

McGarvey, Ronald G.; Rieksts, Brian Q.; Ventura, José A.; Ahn, Namsu

doi:10.1016/j.dam.2015.11.008

Cited by 4 publications

(8 citation statements)

References 37 publications

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“…A related problem extensively studied in the literature is the minimum broadcast graph problem [9,20]. A broadcast graph supports a broadcast from any node to all other nodes in optimal time ⌈log n⌉.…”

Section: Literature Overviewmentioning

confidence: 99%

“…Information dissemination processes studied in the mathematical and algorithmic literature [8,10,15,17] often fall into one of the categories gossiping or broadcasting. When all network nodes control each their unique piece of information, and all pieces are to be disseminated to all nodes, the process is called gossiping [2,3] Dissemination of the information controlled by one particular source node to all network nodes is referred to as broadcasting [20,23], and multicasting [1] if a subset of the network nodes are information targets. If the information is to be stored at the source, and assembled by pieces stored at all other nodes, then the information flows in the reverse of the broadcasting direction, and the dissemination process is accumulation.…”

Section: Introductionmentioning

confidence: 99%

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Strong bounds and exact solutions to the minimum broadcast time problem

Ivanová¹,

Haugland²,

Tvedt³

2021

Preprint

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Given a graph and a subset of its nodes, referred to as source nodes, the minimum broadcast 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 neighbor 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 with sufficiently dense graphs, the lower and upper bounds under study collapse. In instances

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Section: Literature Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong bounds and exact solutions to the minimum broadcast time problem

Ivanová¹,

Haugland²,

Tvedt³

2021

Preprint

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“…A c-broadcast graph with B c (n) edges is said to be a minimum cbroadcast graph. A time-relaxed c-broadcasting [48] allows additional t time steps. Thus, a time-relaxed c-broadcast graph has broadcast time ⌈log c+1 n⌉ + t.…”

Section: Broadcast Graphsmentioning

confidence: 99%

“…ILP formulations to construct c-broadcast graphs, k-fault tolerant c-broadcast graphs and minimum c-broadcast graphs are presented in [48].…”

Section: Broadcast Graphsmentioning

confidence: 99%

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Shared Multicast Trees in Ad Hoc Wireless Networks

Ivanová

2016

Lecture Notes in Computer Science

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This dissertation is a compilation of six research papers that are focused on three different topics summarized in the text. The first three papers address NP-hard problems arising in ad-hoc wireless communication discussed in Chapter 2. In general, the task is to broadcast a message in a given network of wireless devices while minimizing the power consumption. Problems in this category differ in requirements on the network connectivity, models of power consumption, and the ability of the devices to initiate a signal transmission. Some of the common features of these problems are that a device can simultaneously transmit a signal to all devices within its communication vicinity, and that a signal can travel from its originator to its recipient via multiple intermediate devices. The wireless networks are modeled and studied by means of graph theory. Solution techniques for these problems involve mainly methods of integer linear programming and inexact algorithms with or without performance guarantee. The next paper is focused on the problem of minimum broadcast time. Unlike the previous topic, the devices are in this problem supposed to send a signal to at most one neighbouring device at a time. The objective is to determine a sequence of signal transmission from a given set of source devices to the remaining ones, while minimizing the time needed for spreading the signal. Chapter 3 describes this problem in detail along with several related problems. The minimum broadcast time problem is also studied from the perspective of integer linear programming as well as the inexact algorithm perspective. Continuous relaxations of the ILP models help to evaluate the quality of the studied inexact methods. The stronger the model is, the more accurate assessment it provides. The last two papers are dedicated to problems belonging to path planning for multiple robots discussed in Chapter 4. In general, these problems involve a group of agents (robots) initially deployed in an environment. The task is to find a sequence of their moves so that they reach pre-defined destination locations while optimizing a given criterion such as minimum makespan or minimum total arrival time. The agents' movement must obey a set of given rules. An extension of the problem considers agents divided into two (or more) adversarial teams, where the teams have either symmetric or asymmetric objectives. After introducing the adversarial element, the problem of finding a winning strategy for a given team becomes PSPACE-hard, like many other two player games with alternating turns.

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Broadcast graphs using new dimensional broadcast schemes for Knödel graphs

Harutyunyan

2023

Discrete Applied Mathematics

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Binary linear programming models for robust broadcasting in communication networks

Cited by 4 publications

References 37 publications

Strong bounds and exact solutions to the minimum broadcast time problem

Strong bounds and exact solutions to the minimum broadcast time problem

Shared Multicast Trees in Ad Hoc Wireless Networks

Broadcast graphs using new dimensional broadcast schemes for Knödel graphs

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