Solving the Subset-Sum problem by P systems with active membranes

Jiménez, Mario J. Pérez; Núñez, Agustín Riscos

doi:10.1007/bf03037637

Cited by 52 publications

(29 citation statements)

References 6 publications

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“…The subset sum problem can be formulated as follows [20]: Given a finite set A, a weight function, w : A → N, and a constant s ∈ N, determine whether or not there exists a subset B ⊆ A such that a∈B w(a) = s. This 'yes/no' decision problem has been proved to be NP-hard [21] and has no polynomial time solution so far. However, to the SSP with certain restrictions, polynomial time solutions have been proposed in the last few decades [22].…”

Section: Traceability Setsmentioning

confidence: 99%

Post-hoc User Traceability Analysis in Electronic Toll Pricing Systems

Chen

Fonkwe

Pang

2013

Data Privacy Management and Autonomous Spontaneous Security

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Abstract. Electronic Toll Pricing (ETP), a location-based vehicular service, allows users to pay tolls without stopping or even slowing down their cars. User location records are collected so as to calculate their payments. However, users have privacy concerns as locations are considered as private information. In this paper, we focus on user traceability in ETP systems where anonymous location records are stored by the service providers. Based on user toll payment information, we propose a post-hoc analysis of user traceability, which aims at computing a user's all possible traces. Moreover, we propose several methods to improve the effectiveness of the analysis by combining other contextual information and propose a number of optimisations to improve its efficiency as well. We develop a prototype and evaluate the effectiveness of the analysis by conducting extensive experiments on a number of simulated datasets.

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Section: Traceability Setsmentioning

confidence: 99%

Post-hoc User Traceability Analysis in Electronic Toll Pricing Systems

Chen

Fonkwe

Pang

2013

Data Privacy Management and Autonomous Spontaneous Security

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“…In the framework of AM(−n), efficient uniform solutions to weakly NPcomplete problems (Knapsack [27], Subset Sum [26], Partition [10]), and strongly NP-complete problems (SAT [32], Clique [4], Bin Packing [30], Common Algorithmic Problem [29]) have been obtained.…”

Section: Proposition 4 (Milano Theorem)mentioning

confidence: 99%

A Computational Complexity Theory in Membrane Computing

Pérez–Jiménez

2010

Membrane Computing

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Summary. In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with different models of cell-like and tissue-like membrane systems are defined and the most relevant results obtained so far are presented. Many attractive characterizations of P = NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.

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“…Different efficient uniform solutions have been obtained in the framework of recognizer P systems with active membranes, with polarizations and using division rules for elementary membranes: (a) some weakly NP-complete problems solvable in polynomial time in that framework are the following: Knapsack [3], Subset Sum [2], Partition [5]; and (b) some strongly NP-complete problems solvable in polynomial time are the following: SAT [20], Clique [21], Bin Packing [4], Common Algorithmic Problem [6].…”

Section: Recognizer P Systems With Active Membranes and Without Polarmentioning

confidence: 99%

Computational efficiency of dissolution rules in membrane systems

Gutiérrez–Naranjo

Pérez–Jiménez

Riscos–Núñez

et al. 2006

International Journal of Computer Mathematics

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Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to efficiently solve computationally hard problems. On the one hand, an exponential number of objects generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time. On the other hand, when an exponential number of membranes is created and used as workspace, the situation is very different. Two operations in P systems (membrane division and membrane creation) capable of constructing an exponential number of membranes in linear time are studied in this paper. NP-complete problems can be solved in polynomial time using P systems with active membranes and with polarizations, but when electrical charges are not used, then dissolution rules turn out to be very important. We show that in the framework of P systems with active membranes but without polarizations and in the framework of P systems with membrane creation, dissolution rules play a crucial role from the computational efficiency point of view.

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Solving the Subset-Sum problem by P systems with active membranes

Cited by 52 publications

References 6 publications

Post-hoc User Traceability Analysis in Electronic Toll Pricing Systems

Post-hoc User Traceability Analysis in Electronic Toll Pricing Systems

A Computational Complexity Theory in Membrane Computing

Computational efficiency of dissolution rules in membrane systems

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