Compact Integer Programming Models for Power-optimal Trees in Ad Hoc Wireless Networks

Haugland, Dag; Yuan, Di

doi:10.1007/978-1-4419-6111-2_10

Cited by 5 publications

(17 citation statements)

References 39 publications

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“…The mean power for link (i, j) to have successful transmission isp ij (the no-uncertainty power), and the normal random variable describing the uncertainty in the power is p ij . 1 The mean and variance for each link, along with the desired probability of link connectivity, are inputs to the optimization.…”

Section: Approach and Problem Definitionmentioning

confidence: 99%

“…The MET problem can be transformed into an equivalent Steiner tree problem and is thus NP-complete [1].…”

Section: Approach and Problem Definitionmentioning

confidence: 99%

“…Here we summarize a compact integer programming model for MET introduced by Haugland and Yuan [1]; our notation matches theirs. The strength of "MET-F2" over previous formulations comes from multi-commodity flows: each commodity corresponds to a unique destination.…”

Section: A Met-f2 Milp Formulationmentioning

confidence: 99%

“…As shorthand, the subscript (i, k) defines the variables in non-decreasing order of power required, where k refers to the kth-closest node to node i. The formal problem is [1]:…”

Section: A Met-f2 Milp Formulationmentioning

confidence: 99%

“…We base our approach on the multicommodity MET-F2 formulation by Haugland and Yuan [1], and the main idea is to use robust convex optimization to account for uncertainty in required power levels for acomms. We give the problem statement in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Robust minimum energy wireless routing for underwater acoustic communication networks

Reed¹,

Stojanovic

Mitra

et al. 2012

2012 IEEE Globecom Workshops

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Abstract-Marine robots are an increasingly attractive means for observing and monitoring the ocean, but underwater acoustic communications remain a major challenge. The channel exhibits long delay spreads with frequency-dependent attenuation; moreover, it is time-varying. We consider the minimum energy wireless transmission problem [MET], augmented by the practical condition that constraints on link power must be satisfied in probability. For this, we formulate the robust counterpart of the multicommodity mixed-integer linear programming (MILP) model from Haugland and Yuan [1], and derive scaled power levels that account for uncertainty. Our main result is that the deterministic formulation with these scaled power levels recovers exactly the optimal robust solution in the absence of correlations, and therefore allows for efficient solution via MILP. This approach achieves significant power improvements over heuristics, and naturally lends itself to vehicle networks.

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Section: Approach and Problem Definitionmentioning

confidence: 99%

“…The MET problem can be transformed into an equivalent Steiner tree problem and is thus NP-complete [1].…”

Section: Approach and Problem Definitionmentioning

confidence: 99%

Section: A Met-f2 Milp Formulationmentioning

confidence: 99%

“…As shorthand, the subscript (i, k) defines the variables in non-decreasing order of power required, where k refers to the kth-closest node to node i. The formal problem is [1]:…”

Section: A Met-f2 Milp Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust minimum energy wireless routing for underwater acoustic communication networks

Reed¹,

Stojanovic

Mitra

et al. 2012

2012 IEEE Globecom Workshops

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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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Integer programming formulations for the shared multicast tree problem

Ivanová

Haugland

2019

J Comb Optim

Self Cite

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We study the Shared Multicast Tree (SMT) problem in wireless networks. To support a multicast session between a set of network nodes, SMT aims to establish a wireless connection between them, such that the total energy consumption is minimized. All destinations of the multicast message must be connected, while non-destinations are optional nodes that can be used to relay messages. The objective function reflecting power consumption distinguishes SMT clearly from the traditional minimum Steiner tree problem. We develop two integer programming formulations for SMT. Both models are subsequently extended and strengthened. Theorems on relations between the LP bounds corresponding to the models are stated and proved. As the number of variables in the strongest formulations is a polynomial of degree four in the number of network nodes, the models are impractical for computing lower bounds in instances beyond a fairly small size, and therefore a constraint generation scheme is developed. Results from computational experiments with the models demonstrate good promise of the approaches taken.

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Compact Integer Programming Models for Power-optimal Trees in Ad Hoc Wireless Networks

Cited by 5 publications

References 39 publications

Robust minimum energy wireless routing for underwater acoustic communication networks

Robust minimum energy wireless routing for underwater acoustic communication networks

Shared Multicast Trees in Ad Hoc Wireless Networks

Integer programming formulations for the shared multicast tree problem

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