Other Knapsack Problems

Kellerer, Hans; Pferschy, Ulrich; Pisinger, David

doi:10.1007/978-3-540-24777-7_13

Cited by 111 publications

(211 citation statements)

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“…We will next design a dynamic optimization algorithm based on the MCKP [14] as described in the following section. The optimal relay selection and resource allocation are obtained under the constrained bandwidth of the V2V links.…”

Section: Problem Formulationmentioning

confidence: 99%

A novel link allocation method for vehicle‐to‐vehicle‐based relaying networks

Zheng

Long

et al. 2014

Trans Emerging Tel Tech

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Vehicle‐to‐infrastructure (V2I) and vehicle‐to‐vehicle (V2V) are two main communication modes in vehicular ad‐hoc networks. V2V is one of the key techniques to enhance the coverage and capacity of the V2I communication system. In this paper, we propose a novel link allocation method involving both V2I and V2V communications to enhance the throughput of the V2V‐based relaying network. Jointing the links scheduling and radio resource allocation to V2V links is an Non‐deterministic Polynomial (NP) hard problem with huge complexity. The proposed scheduling scheme adopts a dynamic optimization algorithm based on the multi‐choice knapsack problem to solve the problem with acceptable complexity. Simulation results demonstrate that the proposed scheme significantly improves throughput of vehicular networks and achieves higher fairness. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Problem Formulationmentioning

confidence: 99%

A novel link allocation method for vehicle‐to‐vehicle‐based relaying networks

Zheng

Long

et al. 2014

Trans Emerging Tel Tech

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“…The summation in constraint in Equation (21) ensures that a user can at most allocate one channel, while q n 2 f0; 1g K n ensures that a user cannot use half of one channel and half of another channel. The constraint in Equation (20) ensures that if user n transmits on channel k, the SINR of this channel is equal or greater than the SINR constraint c n . It also ensures that if channel k is not used, this constraint is automatically satisfied.…”

Section: Problem Formulationmentioning

confidence: 99%

“…This is a 0; 1 integer problem, which is NP hard. This can be shown by noticing that the problem in Equations (19)-(21) can be viewed as a multidimensional 0; 1 knapsack problem, which is an NP-hard optimisation problem [20].…”

Section: Problem Formulationmentioning

confidence: 99%

Frequency allocation game in satisfaction form

Ellingsæter

2013

Trans. Emerging Tel. Tech.

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In this paper, we analyse frequency allocation in wireless networks through a game in satisfaction form. Satisfaction form games are games without any optimisation aspects where a player is either satisfied or not. We show that such a formulation is especially suited for frequency allocation with quality-of-service constraints. We investigate different equilibrium concepts and show that there exists a mixed-strategy distribution where all players are satisfied with a probability not less than a certain threshold. In the case where there exists a pure-strategy action profile that can achieve satisfaction for all players, we present a learning algorithm that guarantees convergence to this action profile in finite time. In the case that no such pure-strategy action profile exists, we show that the satisfaction form formulation possesses an action profile yielding higher utility for unsatisfied players compared with a normal form game. Lastly we show extensive simulation results that highlight the differences between a frequency allocation game in satisfaction form compared with other game formulations.

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“…SKP, also called bounded setup knapsack problem in McLay and Jacobson (2007a), can be viewed as a variant of the well-known classical knapsack problem (cf., Kellerer et al, 2004). An instance of SKP consists of packing a subset of m item types in a knapsack of capacity c, where each item type has a profit p i , a weight w i , and a (demand) bound n i ≥ 1, for i = 1, .…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of the setup knapsack problem to perturbation of arbitrary profits or weights

Al-Maliky

Hifi

Mhalla

2017

Int Trans Operational Res

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The setup knapsack problem can be viewed as a more complex version of the well‐known classical knapsack problem. An instance of such a problem may be defined by a set scriptN of n items that is divided into m different classes Fi,1≤i≤m. For each class, only one item is considered as a setup item. The aim of the problem is to pack a subset of items in a knapsack of a predefined capacity that maximizes an objective function. In this paper, we analyze the sensitivity of an optimal solution depending on the variation of the profits or weights of arbitrary items. The optimality of the solution at hand is guaranteed by establishing the sensitivity interval that is characterized by both lower and upper values (called limits). First, two cases are distinguished when varying the profits: perturbation of the profit of an item (either ordinary or setup item) and, variation of the profits of a couple of items containing both setup and ordinary items belonging to the same class. Second, two cases are studied, where the perturbation concerns the weights: the variation is relied on the weight of an item and, the case of the variation of the weights of a subset of items. The established results are first illustrated throughout a didactic example, where both approximate and exact methods are used for analyzing the quality of the proposed results. Finally, an extended experimental part is proposed in order to evaluate the effectiveness of the proposed limits.

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Other Knapsack Problems

Cited by 111 publications

References 0 publications

A novel link allocation method for vehicle‐to‐vehicle‐based relaying networks

A novel link allocation method for vehicle‐to‐vehicle‐based relaying networks

Frequency allocation game in satisfaction form

Sensitivity analysis of the setup knapsack problem to perturbation of arbitrary profits or weights

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