IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 15, No. 4, August 2026, pp. 3614 3624 ISSN: 2252-8938, DOI: 10.11591/ijai.v15.i4.pp3614-3624 3614 Smart parking management system: a seamless parking solution using Y OLO and QR code payment technology Sumit K umar 1 , Ruchi Rani 2 , Sanjee v K umar Pippal 3 1 Department of Articial Intelligence and Machine Learning, Symbiosis Institute of T echnology Pune, Symbiosis International (Deemed Uni v ersity), Pune, India 2 Department of Computer Engineering and T echnology , School of Computer Science and Engineering, Dr .V ishw anath Karad MIT W orld Peace Uni v ersity , Pune, India 3 School of Computer Science and Information T echnology , Noida Institute of Engineering and T echnology , Greater Noida, India Article Inf o Article history: Recei v ed Jan 28, 2025 Re vised May 13, 2026 Accepted May 24, 2026 K eyw ords: Deep learning License plate recognition Object recognition Smart parking system Y ou only look once v ersion 5 ABSTRA CT The inef ciencies of traditional parking systems, including manual entry and reliance on sensors, as well as slo w payment lines, contrib ute to congestion and a lo wer le v el of user satisf action. This paper suggests a smart parking management system (SPMS) based on the license plate recognition (LPR) technology using you only look once v ersion 5 (Y OLOv5) model in combination with a QR code based payment system, to automate the parking system. It’ s able to detect v ehicle license plates in real-time, which means that data doesn’ t ha v e to be entered manually , and it also a v oids the need for ph ysical sensors, which cuts do wn on infrastructure costs. W ith a centralized database, the ef cient tracki ng of v ehicles is achie v ed, and QR-based payment will f acilitate contactless payments at e xit. Experimental e v aluation sho ws that the proposed system out performs than the other systems, with an accurac y of 98.09% and recall of 98.25% in case of LPR. This system drastically decreases processing time, c ongestion and impro v es o v erall user e xperience. SPMS is more ef cient, scalable, and reliable than tradit ional and e xisting smart parking systems. The results sho w that the proposed method is a cost-ef fecti v e and practical solution for solving the modern parking management problem. This is an open access article under the CC BY -SA license . Corresponding A uthor: Sumit K umar Department of Articial Intelligence and Machine Learning, Symbiosis Institute of T echnology Pune Symbiosis International (Deemed Uni v ersity) Pune 412115, Maharashtra, India Email: er .sumitkumar21@gmail.com 1. INTR ODUCTION As urban areas e xpand and v ehicle o wnership rises, parking management has become a signicant challenge for city planners and residents. T raditional systems of parking that use manual entry for license plate numbers and older payment methods ha v e reached a stage where the y are becoming completely unrealistic for modernized urban centers. These systems are prone to errors, re v enue losses, and inef ciencies in operations. Manual processes in recording car information tend to be error -prone, and traditional payment methods are usually slo w and incon v enient [1], [2]. Recent technological adv ancements introduce promising alternati v es to traditional approaches. Automation, articial intelligence (AI), and real-time data processing can transform parking management because the y enhance the f acilities’ accurac y , ef cienc y , and con v enience [3], [4]. F or e xample, li cense plate recognition (LPR) technology is an automatic number -pla te recognition system that has J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 3615 been re v ealed to be a promising application that assists in tracing and tracking v ehicles, which reads license plates accurately and quickly without human interv ention [5], [6]. In addition, the de v elopment of payment technologies, such as QR codes, has made the check out process much more ef c ient, with contactless payment options, minimizing w ai ting time and better satisf action to w ards usage [7], [8]. Such inte gration of these technologies into a unied automated parking solution presents a big step forw ard in o v ercoming the e xisting limitations of traditional parking systems. Adv anced algorithms and automation create more possibilities for ef cienc y in parki n g, reduced operational costs, and seamless e xperience for users and operators alik e [9], [10]. Such technology-dri v en solutions are essential for modernizing current urban parking infrastructure to adapt to the needs of e v er -changing city en vironments. One of the major problems with con v entional parking management systems, which depend on hands-on mechanics and outdated technology , is that license plate numbers are entered manually in these mechanisms, making it erroneous and increasing inaccurac y in tracking the v ehicle leading to re v enue leakage [11], [12]. Inef cient payment methods, such as cash and card terminals, create long w ait times that users do not appreciate [13]. Furthermore, the ph ysical sensors and the comple xity of this infrastructure increase the costs of maintenance and hampers system management [14]. It contrib utes as much to reduce operational ef cienc y as it lo wering the quality of the genera l parking e xperience in urban areas. As cities e xpand, the numbers mount, and as v ehicle re gistrations gro w , the insurm ountable limitations of such systems be gin to pre v ail better and assume a ne w solution ur gently . Moreo v er , supporting these decits is necessary for urban parking management to a v oid congestion, loss of re v enues, and user incon v enience. Therefore, some inno v ati v e approaches in v olving technology are required [15], [16]. T o o v ercome the dra wbacks of the traditional parking management system, the automated parking solution proposes the inte gration of adv anced technologies to impro v e ef cienc y , accurac y , and user con v enience. The proposed system has automatic license plate recognition (ALPR) using the you only look once v ersion 5 (Y OLOv5) model to capture the number of license plates with a high le v el of precision at the entry point for each v ehicle. This implies that there is no pro vision for manual data entry in this automated system, thus eliminating error possibilities and ensuring accurate billing [17], [18]. The system emplo ys a sensor -free infrastructure, capturing only the plate number from the v ehicle to track, thus simplifying the system’ s architecture and reducing maintenance costs [19]. T o enhance the user e xperience e v en further , QR code payment has also been incorporated into the system at the e xit, which mak es payment e v en simpler and reduces w aiting time at booths [20], [21]. All these technologies are inte grated, allo wing an optimal use of the space, and making operat ions more ef cient and pleasant for users and operators. The simulations sho wed that the system w as able to ef fecti v ely alle viate congestion and impro v e re v enues [22], [23]. This ne w solution can thus be used to successfully solv e the ne w challenges of parking: parking f acilities in the cities of the future. The main goal of the proposed smart parking management system (SPMS) is to create an intel ligent and automated approach to impro v e the ef cienc y , accurac y , and user e xperience in today’ s parking landscapes. It uses state-of-the-art technology , including Y OLOv5-based ALPR, for rapid and accurate v ehicle recognition at access points, eliminating manual data entry and mitig ating human error . It is an infrastructure that does not require an y sensor to use the v ehicle license plate information to track v ehicles, which reduces the comple xity of the system and lo wers maintenance costs. Besides, QR c od e payment will be incorporated at the e xit, which will create a seamless, contactless, and ef cient payment process, a v oiding the need to ha v e payment stations and reduce payment time. In addition, the proposed system is designed for space optimization and ef cient o v erall operations, which will allo w the system to manage parking resources ef fecti v ely and contrib ute to an enhanced user e xperience, both for the operators and v ehicle o wners. The remainder of this paper is or g anized as follo ws. Section 2 deals with the state of the art of parking techniques. Section 3 describes the methodology of the SPMS m od e l. Section 4 presents and discusses the results. Finally , section 5 concludes the paper . 2. LITERA TURE REVIEW W ith the de v elopment of smart parking management, man y inno v ati v e solutions ha v e been proposed to solv e urban parking problems. These approaches utilize adv anced technologies such as internet of things (IoT), deep learning, and automated systems to enhance parking solutions’ ef cienc y , con v enience, and sustainability . Here is a comparison of some note w orth y rec ent literature contrib utions a v ailable in T able 1. It of fers a clear Smart parking mana g ement system: a seamless parking solution using Y OLO and QR ... (Sumit K umar) Evaluation Warning : The document was created with Spire.PDF for Python.
3616 ISSN: 2252-8938 e xample of the dif ferent technologies and model s used, of the main characteristics of each study , and of the main contrib utions of each, thereby highlighting the state of research and the di v ersity of strate gies used to impro v e parking management systems. T able 1. Literature re vie w of parking management systems Ref. Model used Characteristics Adv antages [1] Backcasting approach Reuse and reallocation of parking and roadspace Polic y measures for autonomous v ehicle (A V) implementation and urban planning [2] Android app with IoT module Real-time parking space notication and reserv ation Lo w-cost enterprise solution for smart parking [3] Dynamic and proacti v e planning system Sensor technology and automated carriers Impro v ed operational ef cienc y via simulation–optimization [4] V arious sensors and data analysis Occupanc y detection and dynamic pricing Challenges and opportunities in implementing smart parking [5] V arious inno v ations and technologies Unb undling parking costs and reducing minimums Identies and outlines v e k e y de v elopments in parking [6] W illingness to pay (WTP) model Hypothetical permit program and double hurdle model Estimates residents’ WTP for parking permits [7] Open source computer vision library (OpenCV), nump y library and ArUco mark ers Measurement of v ehicle size and real-time detection Ef cient space allocation and v ehicle monitoring [8] Deep learning-based object detection LPR and disability badge v erication Ef cient and real-time management of accessible parking spaces [9] Con v olutional neural netw orks (CNN) Image classication, localization, and detection Role of deep learning in visual recognition systems [10] Y OLOv5 for v ehicle detection Real-time performance and high accurac y Scalable and ef cient data-dri v en parking solution [11] Y OLO-based model Real-time detection and number plate recognition High accurac y in v ehicle and plate detection [12] Y OLOv5l, con v olutional recurrent neur al netw ork (CRNN) and adapti v e feature fusion netw ork (AFF-Net) High accurac y and cloud deplo yment Rob ust LPR system for outdoor parking toll [13] Y OLOv5 neural netw orks Real-time v ehicle detection and f alse count pre v ention Ef cient real-time v ehicle video detection [14] Raspberry Pi and deep learning tools Real-time a v ailability and automatic billing Cost-ef fecti v e and time-sa ving smart parking solution [15] IoT and v arious smart applications Adv ance reserv ation and cashless billing Comprehensi v e features for smart city inte gration 3. METHOD The SPMS is designed with an emphasis on automation, ef cienc y , and user con v enience. The system architecture is di vided into four modules: admin panel, LPR, user entry , and user e xit. These modules w ork in tandem to pro vide a seamless parking e xperience. The core components of this model include the Y OLOv5 [22]–[26] model for ALPR, a centralized databas e for v ehicle tracking, and a QR code-based payment system. Figure 1 demonstrates the SPMS. The admin panel manages parking lots, congures fees, and tracks space a v ailability in real-time. LPR automates v ehicle license plate number e xtraction and database entries. QR code-based payment mak es it con v enient for users to mak e payments. The system completes the payment using a QR code when the user lea v es. This process mak es controlling traf c mo v ements in parking zones easier and impro v es operational ef cienc y . In this module, a good quality camera is used to capture the v ehicle license plate at the entrance, which guarantee a high-resolution image carrying all essential details of that image, which is the foremost thing for image processing. Figure 2 demonstrates the w orking of the LPR module. After capturing the license plate images, some preprocessing techniques are applied to the pictures as the captured images are in the form of red, green, and blue (RGB), which is con v erted into grayscale. Dif ferent ltering techniques remo v e noise from the pictures to impro v e the picture quality . Images are resized into a particular format afterw ard. Image resizing smoothens processing by the CNN. CNN architecture is emplo yed to identify license plate r e gi o ns . It e xtracts rele v ant features specic to the license plates. Pooling layers reduce the dimensionality of e xtracted feature maps and the rectied linear unit (ReLU) acti v ation function is used to learn comple x patterns in images. Dropout layers are used to reduce Int J Artif Intell, V ol. 15, No. 4, August 2026: 3614–3624 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 3617 the o v ertting of the model. Once the license plate has been detected, indi vidual characters are se gmented from that plate re gion. The se gmented characters are then passed through an optical character recognition (OCR) engine that con v erts them to alphanumeric te xt. The e xact license plate number is the system’ s nal output. The e xtracted te xt and alphanumeric characters automatically get written into the database along with the timestamp of the user who made the request and selected block information. This process is automated, eradicating the need to manually input data and ensuring the v ehicle’ s entry and e xit times timestamping. Figure 1. SPMS methodology Figure 2. LPR modules As soon as the user steps into the parking area, LPR is automatically in v ok ed, wherein the number plate will be identi ed and the number pick ed up. F ollo wing this, the user will be ask ed to choose a parking Smart parking mana g ement system: a seamless parking solution using Y OLO and QR ... (Sumit K umar) Evaluation Warning : The document was created with Spire.PDF for Python.
3618 ISSN: 2252-8938 block. Three attempts are gi v en to the user to arri v e at the correct block. F or e v ery attempt performed, an alternati v e block is returned. If the user refuses the three options, the block automatically gets assigned. After determining the block, it inserts the database entry and its timestamp. The occupied and a v ailable blocks are displayed on the screen for the user . At the e xit, the dynamic QR code is displayed on the light emitting diode (LED) screen. The parking fee is calculated based on the period a v ehicle has been k ept in the parking by computing the dif ference in timestamp v alues from the entry to e xit time stamp. Although the parking fee w as computed hourly , the payment can be managed with the help of the abo v e-mentioned QR code through v ery rapid contactless payments without an y cash handling. Once payment is conrmed, the barrier opens and the v ehicle is free to lea v e. The Y OLO architecture, as sho wn in Figure 3, is b uil t around a sequence of con v olutional layers that progressi v ely e xtract visual features, supported by residual connections that help retain information across deeper layers. Max pooling reduces spatial comple xity , while concatenation layers mer ge feature maps from dif ferent stages to preserv e both ne-grained and high-le v el details. Figure 4 presents the use case diagram for the SPMS, outlining the k e y interactions between users, v ehicles, and the system across entry , payment, and e xit scenarios. Figure 3. Y OLO architecture Figure 4. Use case diagram There a re tw o users in the system: the admin and the user . The admin manages and congures the system; therefore, it has all the needed permissions. The ’enter parking lot’ acti vity describes the o w of entering a parking lot. In t his acti vity , the user chooses a parking block by selecting one, then goes and looks for his v ehicle in a gi v en spot by scanning it in. The ’e xit parking lot’ acti vity describes the user’ s e xit process. The user scans a dynamic QR code to settle his payment before lea ving the parking lot. The receipt is generated after the e xit and a QR code for the payment are issued. After scanning t h e code at the payment, the v ehicle is released from the parking lot. Such an automated system will sa v e managers and car o wners much time by cutting of f human interference in managing permits. The system tracks v ehicles using ALPR technology Int J Artif Intell, V ol. 15, No. 4, August 2026: 3614–3624 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 3619 without a sensor . By doing this, ground loops and other con v enti onal parking sensors—prone to wear and tear and necessitate frequent maintenance and replacement costs—are no longer necessary . The SPMS system simplies infrastructure setup and reduces long-term maintenance requirements by using LPR data for v ehicle identication and tracking throughout the parking duration. This approach enhances user con v enience and eliminates errors associated with manual data entry , impro ving data accurac y for billing and tracking purposes. T ar get detection using the Y OLO model, the system identies the v ehicle at the entrance by using Y OLO for real-time object detection. The single-stage approach mak es Y OLO more computationally ef cient and allo ws the video stream from the camera at the entrance to be processed in real-time. Once the user e xits the parking lot, a QR code will appear on the screen. Users automatically connect to a secure payment site by scanning a QR code with their smartphone. This eliminates traditional payments and w aiting times. The QR code payment system also simplies the payment process for emplo yees and reduces the comple xity of managing cash or ph ysical payment f acilities. Figure 5 sho ws the o v erall w orko w of the system. The diagram sho ws the detection of the li cense plate; if the license plate is not detected, a repeti tion of t h e proces s i s perf o r med, follo wed by inserting the detected license plate in the database, further calculating the time of the v ehicle as the user selects the slot. The main interf ace of the v ehicle parking system gi v es a li v e vie w of all parking slots, clearly sho wing which spots are tak en and which are free. Free slots are highlighted in green, while occupied ones appear in red. The panel on the left w alks through the v ehicle entry process. The user selects a car image, and the LPR module, po wered by Y OLO, automatically reads the plate number and sa v es it to the system database. The right-side windo w demonstrates the e xit process, displaying the current v ehicles par k ed. Upon clicking the e xit b utton, a QR code is generated. When a user scans the QR code, a summary , including the payable amount, is pro vided to the user . Figure 5. W orko w diagram of the system Smart parking mana g ement system: a seamless parking solution using Y OLO and QR ... (Sumit K umar) Evaluation Warning : The document was created with Spire.PDF for Python.
3620 ISSN: 2252-8938 4. RESUL TS AND DISCUSSION The performance of the proposed SPMS meets and e v en outperforms in certain aspects the pre vious studies related to intelligent parking and LPR. Recently , deep learning-based LPR methods, such as Y OLO v ariants and CNN-based methods [9], ha v e achie v ed high accurac y of 95%–98% based on the comple xity of the dataset and the en vironment in which the y are applied. F or e xample, Y OLO-based LPR models [10]–[13] ha v e pro v en to be ef cient and rob ust for real-time license plate detection in controlled conditions, b ut their performance drops slightly in the real w orld where lighting changes, occlusion and m otion blur e xist. In contrast, the accurac y and recall of the proposed system are 98.09% and 98.25%, respecti v ely , which are competiti v e and reliable results e v en in practical considerations. Moreo v er , pre vious studies on smart parking systems using IoT and image processing technologies [15] ha v e pointed out the benets of impro v ement in the automation of the parking system and the reduction of congestion, b ut man y of these systems are based on sensor -based infras tructures or semi-automated w ork o ws, adding to maintenance costs and system comple xity . The proposed SPMS, on the other hand, reduces the dependenc y on ph ysical sensors, uses vision based LPR and reduces infrastructure o v erhead while maintaining high accurac y . Besides, the use of QR code for payment has been considered in some recent studies on smart mobility as a w ay to impro v e the ease of use for users, b ut in the pre vious ones it is not widely connected to capabilities of real-time LPR and automatic slot allocation. The proposed system outperforms the e xisting syst ems in terms of pro viding a more comprehensi v e and more scalable solution, where the Y OLO-based LPR, automated database management and contactless QR-based payment are considered. The results of this study further conrm that the proposed SPMS is not only consistent with the state-of-the-art methodologies b ut also to pro vide an impro v ement re g arding operational ef cienc y , human interv ention reduction and user e xperience. The performance comparison sho wn in Figure 6 demonstrates that the proposed SPMS achie v es superior res u l ts compared to e xisting systems. The model attains an accurac y of 98.09% and a recall of 98.25%, which are signicantly higher than traditional approaches. This impro v ement is primarily attrib uted to the use of the Y OLO-based LPR module, which ensures ef cient and precise detection in real-time scenarios. The results v alidate the rob ustness and reliability of the proposed system. Figure 6. Performance comparison of the proposed SPMS with e xisting systems A comparati v e analysis of bot h the traditional parking system and the proposed SPMS is sho wn in Figure 7 with re g ard to v arious performance objecti v es dimensions lik e ef cienc y , accurac y , and the satisf action of the user . The automated w orko w , minimal human in v olv ement and real-time processing of the SPMS mak e it a signicant impro v ement o v er the traditional system. QR code payment and ALPR are also inte grated into impro v e the user e xperience and reduce the w orkload. Int J Artif Intell, V ol. 15, No. 4, August 2026: 3614–3624 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 3621 The comparison process ing time of the proposed SPMS and other traditional methods presented in Figure 8 points out the ef cienc y of the proposed method in minimizing the processing time. The system can substantially reduce the w aiting time for v ehicles to enter , pay for , and lea v e parking spaces from the con v entional parking mode. Through the use of automated LPR and contactless QR code payment, the system eliminates manual operations and reduces w aiting time, thus promoting a seamless and ef cient traf c o w in the parking area. Figure 7. Comparison of traditional parking system and proposed SPMS Figure 8. Processing time comparison between traditional parking system and SPMS Smart parking mana g ement system: a seamless parking solution using Y OLO and QR ... (Sumit K umar) Evaluation Warning : The document was created with Spire.PDF for Python.
3622 ISSN: 2252-8938 In T able 2, the comparisons of the SPMS and the traditional parking management system are sho wn with adv antages and disadv antages. From the table, it is e vident that t he system outperforms traditional systems in man y respects. The ef fecti v eness of the LPR system has been v eri ed since the related accurac y and recall rates are quite high. QR code payment automation helps to complete the process with fe wer human errors and increased user satisf action. The syst em utilizes optimal space and generates more re v enue through well-designed systems. Ho we v er , the system has disadv antages such as a higher initial cost and greater reliance on technology than con v entional systems. Despite these issues, the all-around benets in ef cienc y , accurac y , and user -friendliness point to a highly desirable system compared with con v entional parking management approaches. T able 2. Comparison of proposed SPMS and traditional parking system Feature SPMS T raditional parking system License plate entry ALPR using Y OLO model Manual entry P ayment method QR code payment P ayment centers with cash or card Ef cienc y High, streamlined process Lo w , manual processes Human error Minimal, automated system High, prone to mistak es Congestion Reduced Higher due to manual operations User satisf action Increased Lo wer Con v enience High, due to automation and QR code payment Lo w , manual processes and payment centers Accurac y High V ariable, depends on manual input Initial cost High Lo w T echnology dependenc y High Lo w Space utilization Optimized Less optimized Re v enue generation Increased due to ef cienc y and optimized space use Standard, depends on usage Adaptability and capacity b uilding Potential for high adaptability and capacity b uilding with further impro v ements Limited 5. CONCLUSION This study proposes a ne w SPMS that tak es the concept of traditional parking to the ne xt le v el with adv anced technologies. SPMS of fers ALPR technology with Y OLO models, which f acilitates v ehicle tracking and billing while minimizing the comple xity of processes by lo wering the need of manual entry operations. The parking e xperience has been enhanced, and customer con v enience has been impro v ed with QR code payment. Through e xtensi v e simulation and real w orld e x ecutions, it has been demonstrated that SPMS can sa v e mone y , generate re v enue, and enhance customer satisf action. The e xploration also of fers man y benets for parking system optimization, as it of fers a ne w f ashion and can ha v e the potential to be widely used in ci vic conte xts. Ov erall, the SPMS is a signicant adv ancement in parking solutions, pro viding a more ef cient and en vironmentally friendly w ay to address the challenge of parking in modern cities. The results highlight the signicant changes that can be achie v ed by incorporating state-of-the-art technologies into parking systems. The y are als o used to illustrate the w ay automated syst ems can solv e the problems f aced by traditional systems and to open the w ay for ne w inno v ations in urban transport infrastructure. The ndings of the study pro vide researchers with suggestions for i mpro vi ng the accurac y and ef cienc y something that can be used in smart city technologies. The decongesti v e, con v enient and re v enue generating properties of the SPMS are v ery benecial to the community . The system will re-engineer parking and enhance user e xperience in an y urban setting to mak e it manageable and ef cient. In the future, impro v ements might be needed for the system so that real-time data analytics and machi ne learning algorithms can be applied to better f acilitate dynamic parking management and predicti v e analytics. Additional research into scalability will help to further impro v e ef cienc y of dif ferent urban and types of parking f acilities. Further impro v ement can be made through dynamic pricing (based on demand) and adv anced analytics (based on users) that w ould ultimately increase scalability of the system. It will help maintain the SPMS as dynamic and with respect to the gro wing urban parking challenges. FUNDING INFORMA TION No funding in v olv ed. Int J Artif Intell, V ol. 15, No. 4, August 2026: 3614–3624 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 3623 A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the Contrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib utions, reduce authorship disputes, and f acilitate collaboration. Name of A uthor C M So V a F o I R D O E V i Su P Fu Sumit K umar Ruchi Rani Sanjee v K umar Pippal C : C onceptualization I : I n v estig ation V i : V i sualization M : M ethodology R : R esources Su : Su pervision So : So ftw are D : D ata Curation P : P roject Administration V a : V a lidation O : Writing - O riginal Draft Fu : Fu nding Acquisition F o : F o rmal Analysis E : Writing - Re vie w & E diting CONFLICT OF INTEREST ST A TEMENT Authors state no conict of interest. D A T A A V AILABILITY Data a v ailability is not applicable to this paper as no ne w data were created or analyzed in this study . REFERENCES [1] E. G. Gonz ´ alez, S. Nogu ´ es, and D. 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