N-queens Research Articles

A Novel Approach for Solving the N-Queen Problem Using a Non-Sequential Conflict Resolution Algorithm

The N-Queens problem is a fundamental challenge in combinatorial optimization, commonly used as a benchmark for assessing the efficiency of algorithms. Traditional algorithms, such as Backtracking with Forward Checking (BFC), constraint satisfaction problem (CSP) techniques, Lookahead algorithms, and heuristic-based methods, often face challenges with exponential time complexity, making them less practical for large-scale instances. This paper introduces a novel algorithm, non-sequential conflict resolution (NSCR), which improves performance over traditional algorithms through dynamic conflict resolution. The NSCR algorithm iteratively resolves conflicts among queens by adjusting their positions, aiming to optimize both time complexity and memory usage. While NSCR also operates within exponential time bounds, it demonstrates improved scalability and efficiency compared to traditional methods. A significant strength of the NSCR algorithm lies in its space complexity, which is O(n), and a time complexity that, while typically lower than traditional methods, can reach O(n3) in the worst-case scenario. This linear space complexity is highly advantageous, particularly when dealing with large problem sizes, as it ensures efficient use of memory resources. Comparative analysis with the aforementioned algorithms shows that NSCR offers superior resource management, using up to 60% less memory and reducing runtime by approximately 50%, making it an efficient option for large-scale instances of the N-Queens problem. The algorithm’s performance, evaluated on problem sizes ranging from 8 to 1000 queens, highlights its ability to manage computational resources effectively, despite the inherent challenges of exponential time complexity.

High Rates of Honey Bee Colony Losses and Regional Variability in Ethiopia Based on the Standardised COLOSS 2023 Survey.

The COLOSS research association has been assessing honey bee colony losses, associated risk factors and management, focusing on Western countries but with a progressive international expansion. Here, we report the first survey on the loss rates of colonies in 2022/2023 in Ethiopia using COLOSS monitoring survey tools. A face-to-face interview questionnaire survey was conducted on 64 beekeepers selected from Oromia and Tigray regions. This covered 1713 honey bee colonies distributed in 68 apiaries. The percentages of colonies lost were significantly different between Oromia (24.1%) and Tigray (66.4%) regions. Colony losses were attributed as unsolvable queen problems (8% in Oromia; 10% in Tigray), natural disaster (32%; 82%), and empty hives or dead colonies (60%; 8%). The loss rate was significantly affected by queen replacement (p < 0.0001), use of natural comb (p < 0.0001), feed supplementation (p < 0.0001), region (p < 0.0001), varroa treatment (p < 0.0001), colony splitting (p < 0.01), and merging (p < 0.01). Beekeepers in Oromia managed more colonies and implemented improved practices compared to those in Tigray. However, all beekeepers in Oromia detected at least some bees with signs of deformed wing virus, compared to 76% of beekeepers in Tigray. In conclusion, the colony loss rate was significantly different between Oromia and Tigray regions due to differences in natural disasters, management, environment and health factors.

Visualizing Algorithms in the Field of Education: A Comprehensive Review

Abstract: Visualization of algorithms can enhance computer science education by offering a beneficial method for comprehending intricate concepts within engineering courses. An electronic learning tool has been created to cover various algorithms, including sorting algorithms, prime numbers, recursive sorting algorithms, and the N Queen problem. Employing animation as a means of conveying information, the tool enables users to select data ordering and algorithms. Users can either initiate automatic animation or progress through the steps at their own pace. Additionally, the pathfinding algorithm permits usersto modify the starting and ending nodes. This e-learning tool serves as both a standalone application and a complementary resource for in-person training, providing a visual representation of the execution stages of algorithmic rules.

Improved Naked Mole-Rat Algorithm Based on Variable Neighborhood Search for the N-Queens Problem

Solving problems via artificial intelligence techniques has widely prevailed in different aspects. Implementing artificial intelligence optimization algorithms for NP-hard problems is still challenging. In this manuscript, we work on implementing the Naked Mole-Rat Algorithm (NMRA) to solve the n-queens problems and overcome the challenge of applying NMRA to a discrete space set. An improvement of NMRA is applied using the aspect of local search in the Variable Neighborhood Search algorithm (VNS) with 2-opt and 3-opt. Introducing the Naked Mole Rat algorithm based on variable neighborhood search (NMRAVNS) to solve N-queens problems with different sizes. Finding the best solution or set of solutions within a plausible amount of time is the main goal of the NMRAVNS algorithm. The improvement of the proposed algorithm boosts the exploitation capability of the basic NMRA and gives a greater possibility, with the emerging search strategies, to find the global best solution. This algorithm proved successful and outperformed other algorithms and studies with a remarkable target. A detailed comparison is performed, and the data results are presented with the relevant numbers and values. NMRA and NMRAVNS comparisons are implemented and recorded. Later on, a comparison between the Meerkat Clan Algorithm, Genetic Algorithm, Particle Swarm Optimization, and NMRAVNS is tested and presented. Finally, NMRAVNS is evaluated against the examined genetic-based algorithm and listed to prove the success of the proposed algorithm. NMRAVNS outperformed previous findings and scored competitive results with a high number of queen sizes, where an average time reduction reached about 87% of other previous findings.

RESULTS OF HONEY BEE COLONY LOSSES MONITORING IN UKRAINE IN THE CONDITIONS OF WAR AFTER THE WINTER OF 2022-2023

Losses of Western honey bee colonies (Apis mellifera L.) represent a globally significant phenomenon with profound ecological and economic implications, yet the underlying causes remain a subject of ongoing investigation (Insolia et al., 2022). This study aimed to evaluate colony losses following the 2022–2023 wintering season in Ukraine in the conditions of the ongoing war, as part of the annual international monitoring effort coordinated by the COLOSS. The survey was conducted employing the standardized COLOSS protocol and covered all physiographic zones of Ukraine except for the Crimean Mountains, with data from 751 valid protocols synthesized for analysis. The average overall loss rate after the 2022-2023 wintering season in Ukraine was 10.8 %, slightly exceeding the previous year's rate (8.9% after the 2021-2022 wintering season). Notably, the loss of bee colonies (6.55 %) nearly doubled compared to the previous year (3.72% after the 2021-2022 wintering season), while losses due to unsolvable queen problems (3.07 %) remained consistent with the previous year (3.07% after the 2021-2022 wintering season), and losses attributable to adverse natural phenomena (1.27%) decreased by over 1.5 times (2.08% after the 2021-2022 wintering season). The highest overall loss rate of bee colonies was observed in the steppe zone (17.0%), with significantly lower losses in the Ukrainian Carpathians (7.3%), mixed (8.6%), and broad-leaved (9.0%) forest zones. The distribution of loss components across different physiographic zones mirrored the national trend: dead/missing colonies (4.19 % - 10.13 %), unresolved queen issues (2.16 % - 5.24 %), losses due to adverse natural events (0.74 % - 1.85 %). Among the reported characteristics of lost colonies, starvation-induced mortality (19 %) and unexplained bee deaths (17.8 %) were most frequently cited, while bee disappearances (9.1%) and dead bees within hives despite available food (10.4 %) were less common. Over 12% of analysed beekeeping operations were situated in areas affected by armed conflict, with some experiencing direct damage to apiaries (2.4%) and associated equipment (0.1% - 0.5%). Once again, the inverse relationship between apiary size and total losses was reaffirmed, though no correlations between colony losses and migratory beekeeping were identified. 76.4 % of respondents monitored their colonies for Varroa mite infestations, with 97.5% treating for varroosis. Notably, 19.6% of respondents treated their colonies without prior monitoring of mite infestation levels. Amitraz-based veterinary products remained the most commonly used acaricides in Ukraine, applied through fumigation or aerosols (32.2 %) and strips (21.7 %). Additionally, 22.9 % of surveyed beekeepers practiced drone brood removal. The applying of traditional beekeeping methods increased (10,4% this year, compared to 2.18 % and 3.60 % before the wintering seasons of 2020-2021 and 2019-2020, respectively). Keywords: honey bee, Apis mellifera, colony losses, monitoring, mortality, beekeeping, varroosis

N-Rooks and n-queens problem on planar and modular chessboards with hexagonal cells

We show the existence of solutions to the n-rooks problem and n-queens problem on chessboards with hexagonal cells, problems equivalent to certain three and six direction riders on ordinary chessboards. Translating the problems into graph theory problems, we determine the independence number (maximum size of independent set) of rooks graph and queens graph. We consider the $n \times n$ planar diamond-shaped H_n with hexagonal cells, and the board $H_n$ as a flat torus $T_n$. Here, a rook can execute moves on lines perpendicular to the six sides of the cell it is placed, and a queen can execute moves on those lines together with lines through the six corners of the cell it is placed.

Quantum Metropolis Solver: a quantum walks approach to optimization problems

The efficient resolution of optimization problems is one of the key issues in today’s industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to challenge these types of problems. In this paper, we focus on the Metropolis-Hastings quantum algorithm, which is based on quantum walks. We use this algorithm to build a quantum software tool called Quantum Metropolis Solver (QMS). We validate QMS with the N-Queen problem to show a potential quantum advantage in an example that can be easily extrapolated to an Artificial Intelligence domain. We carry out different simulations to validate the performance of QMS and its configuration.

Survey Results of Honey Bee Colony Losses in Winter in China (2009-2021).

There is growing concern that massive loss of honey bees can cause serious negative effects on biodiversity and ecosystems. Surveys of colony losses have been performed worldwide to monitor the dynamic changes and health status of honey bee colonies. Here, we present the results of surveys regarding winter colony losses from 21 provinces in China from 2009 to 2021, with a total of 1,744,324 colonies managed by 13,704 beekeepers. The total colony losses were low (9.84%; 95% Confidence Interval (CI): 9.60-10.08%) but varied among years, provinces, and scales of apiaries. As little is known about the overwintering mortality of Apis cerana, in this study, we surveyed and compared the loss rates between Apis mellifera and A. cerana in China. We found colonies of A. mellifera suffered significantly lower losses than A. cerana in China. Larger apiaries resulted in higher losses in A. mellifera, whereas the opposite was observed in A. cerana. Furthermore, we used generalized linear mixed-effects models (GLMMs) to evaluate the effects of potential risk factors on winter colony losses and found that the operation size, species, migration, migration×species interaction, and queen problems were significantly related to the loss rates. New queens can increase their colony overwintering survival. Migratory beekeepers and large operations reported lower loss rates.

The number of n-queens configurations

The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n×n board. We show that there exists a constant α=1.942±3×10−3 such that Q(n)=((1±o(1))ne−α)n. The constant α is characterized as the solution to a convex optimization problem in P([−1/2,1/2]2), the space of Borel probability measures on the square.The chief innovation is the introduction of limit objects for n-queens configurations, which we call queenons. These form a convex set in P([−1/2,1/2]2). We define an entropy function that counts the number of n-queens configurations that approximate a given queenon. The upper bound uses the entropy method of Radhakrishnan and Linial–Luria. For the lower bound we describe a randomized algorithm that constructs a configuration near a prespecified queenon and whose entropy matches that found in the upper bound. The enumeration of n-queens configurations is then obtained by maximizing the (concave) entropy function in the space of queenons.Along the way we prove a large deviations principle for n-queens configurations that can be used to study their typical structure.

An incremental approach to the n-queen problem with polynomial time

An incremental approach to the n-queen problem with polynomial time

Secure Big Data Transmission based on Modified Reverse Encryption and Genetic Algorithm

The modern systems that have been based upon the hash function are more suitable compared to the conventional systems; however, the complicated algorithms for the generation of the invertible functions have a high level of time consumption. With the use of the GAs, the key strength is enhanced, which results in ultimately making the entire algorithm sufficient. Initially, the process of the key generation is performed by using the results of n-queen problem that is solved by the genetic algorithm, with the use of a random number generator and through the application of the GA operations. Ultimately, the encryption of the data is performed with the use of the Modified Reverse Encryption Algorithm (MREA). It was noticed that the suggested algorithm provided more sufficient results concerning the key and the strength of security. However, it has lower computational efficiency as compared to the other algorithms.

A heuristic based linear time O(N) novel solution to N-Queen problem

N-Queen problem is a classic puzzle in which ‘N’ number of queens and a chessboard of size N X N is given. The puzzle is to lay all the given queens on the chessboard in a way that all queens are safe (i.e., no queen on the chessboard is intersecting the other queen). In this article we have proposed an algorithm to solve the N-Queen puzzle in O(N) time-complexity, without affecting the space-complexity.

AI-eXplained (AI-X) [President’s Message

I have an exciting new development to report to you that has been a joint collaboration between CIS and IEEE staff teams across multiple OUs. Together, we are introducing to the IEEE a new type of article that is being labeled “immersive”. Our original foray into immersive articles will appear in this publication and have an educational orientation. We call the category AI-eXplained (AI-X). Essentially, educators who are building interactive educational software to teach aspects of computational and artificial intelligence can now find a peer reviewed venue for those efforts. This is so cool. A two page extended abstract will appear in both the printed and online versions of the magazine, but the magic happens inside Xplore. The “real” paper is viewed like a supplement and contains all of the immersive components to bring this material to life, allowing the reader to directly interact with the content. It’s much better to experience a concept than to read an explanation. Note the (purposeful) similarity of our name, AIX, to the popular research topic XAI (eXplainable AI). Even though both concern explaining, the difference is that the former is an educational enterprise while the latter is a research topic. The very first such manuscript is in this issue of CIM. The paper is titled “Choosing Representation, Mutation, and Crossover in Evolutionary Algorithms” by Alexander Dockhorn and Simon Lucas (who first posed the challenge to me for CIS to produce interactive articles). Please look at the abstract, but really have some fun trying to solve the 8-Queens problem and explore how one can do it through evolutionary computation in the immersive content. This paper went through a rigorous review process designed for such contributions and will have the same publication credentials as any other published manuscript in CIM

Computing tighter bounds on the n-queens constant via Newton’s method

In recent work Simkin shows that bounds on an exponent occurring in the famous n-queens problem can be evaluated by solving convex optimization problems, allowing him to find bounds far tighter than previously known. In this note we use Simkin’s formulation, a sharper bound developed by Knuth, and a Newton method that scales to large problem instances, to find even sharper bounds.

Honey bee colony loss rates in 37 countries using the COLOSS survey for winter 2019–2020: the combined effects of operation size, migration and queen replacement

This article presents managed honey bee colony loss rates over winter 2019/20 resulting from using the standardised COLOSS questionnaire in 37 countries. Six countries were from outside Europe, including, for the first time in this series of articles, New Zealand. The 30,491 beekeepers outside New Zealand reported 4.5% of colonies with unsolvable queen problems, 11.1% of colonies dead after winter and 2.6% lost through natural disaster. This gave an overall colony winter loss rate of 18.1%, higher than in the previous year. The winter loss rates varied greatly between countries, from 7.4% to 36.5%. 3216 beekeepers from New Zealand managing 297,345 colonies reported 10.5% losses for their 2019 winter (six months earlier than for other, Northern Hemisphere, countries). We modelled the risk of loss as a dead/empty colony or from unresolvable queen problems, for all countries except New Zealand. Overall, larger beekeeping operations with more than 50 colonies experienced significantly lower losses (p < 0.001). Migration was also highly significant (p < 0.001), with lower loss rates for operations migrating their colonies in the previous season. A higher proportion of new queens reduced the risk of colony winter loss (p < 0.001), suggesting that more queen replacement is better. All three factors, operation size, migration and proportion of young queens, were also included in a multivariable main effects quasi-binomial GLM and all three remained highly significant (p < 0.001). Detailed results for each country and overall are given in a table, and a map shows relative risks of winter loss at the regional level.

The n-queens completion problem

An n-queens configuration is a placement of n mutually non-attacking queens on an ntimes n chessboard. The n-queens completion problem, introduced by Nauck in 1850, is to decide whether a given partial configuration can be completed to an n-queens configuration. In this paper, we study an extremal aspect of this question, namely: how small must a partial configuration be so that a completion is always possible? We show that any placement of at most n/60 mutually non-attacking queens can be completed. We also provide partial configurations of roughly n/4 queens that cannot be completed and formulate a number of interesting problems. Our proofs connect the queens problem to rainbow matchings in bipartite graphs and use probabilistic arguments together with linear programming duality.

An Innovative JavaScript-Based Framework for Teaching Backtracking Algorithms Interactively

Algorithm fundamentals are useful to learn at different levels engineering education. One of the most difficult concepts to teach and understand is backtracking algorithms with proper bounding functions. This article proposes a framework to implement interactive online tools showing examples of backtracking algorithms in which students can graphically observe execution step-by-step. This approach is illustrated with the n-queens problem with students from Prince Sultan University, Saudi Arabia, and Complutense University of Madrid, Spain. The results show 6.67% increased learning on a backtracking exercise in the experimental group over the control group, in which the algorithms were automatically validated with DOMjudge software (an automated system used to run programming contests). The proposed framework was evaluated as easy to use, with a score of 74.5% in the validated System Usability Scale (SUS); easy to learn, with a score of 6.22 out of 7 in the validated Usefulness, Satisfaction, and Ease-of-Use (USE) scale; and with a general satisfaction of 5.97 out of 7 in the validated USE scale.

A Generalized Search Construct for Imperative Languages to Facilitate Declarative Programming

Search is one of the more common strategies used by problem-solving agents. For many hard problems, a backtracking search can be the most effective approach for finding a solution. Logic programming languages provide, as a core feature of the language, the mechanics for the search behind the scenes without requiring the user to specify the algorithm. However, this functionality has been generally left out of the core features of imperative programming languages. In this work, we propose integrating a search agent into an imperative programming language through a search construct in the syntax. By doing so, our intention is that the user may apply a declarative approach to problem solving. We extend the Go programming language with this search construct and develop an agent to perform the search. The algorithm behind the search is implicitly handled by the agent. We demonstrate the effectiveness of this search construct through solutions to an exhaustive search over a file-system, the NQueens problem, and the monkey and the bananas problem. To evaluate the performance of our agent, we compare its runtime performance against two of the common Prolog implementations, SWI-Prolog and GNU Prolog.

A Linear Time Pattern Based Algorithm for N-Queens Problem

The n-queens problem is the placing of n number of queens on an nxn chessboard so that no two queens attack each other. This problem is important due to various usage fields such as VLSI testing, traffic control job scheduling, data routing, dead-lock or blockage prevention, digital image processing and parallel memory storage schemes mentioned in the literature. Besides, this problem has been used as a benchmark for developing new Artificial Intelligence search techniques. However, it is known that backtracking algorithms, one of the most frequently used algorithms to solve this problem, cannot produce all solutions in large n values due to the exponentially growing time complexity. Therefore, various methods have been proposed for producing one or more solutions, not all solutions for each n value. In this study, a pattern based approach that produces at least one unique solution for all n values (n&amp;gt;3) was detected. By using this pattern, a new algorithm that produces at least one unique solution for even very large n values in linear time was developed. The developed algorithm with О(n) time complexity produces quite faster solution to n-queens problem and even in some values, this algorithm produces (n-1)/2 unique solutions in linear time.

Generalized Graph Product and its Application on Generating Solutions of the Millennium n-Queens Problem

The generalized Kronecker graph product was introduced by Figueroa-Centeno et al. (2008). Later, Baca et al. (2018) used it for obtaining solutions of the n-queens problem on larger boards from solutions on smaller boards. In this paper, we generalize the graph product and the recent results by Baca et al. (2018), obtaining a larger class of solutions by knowing solutions on lower size boards in advance. We finalize the paper stating a couple of conjectures regarding conditions for obtaining composite solutions via graph product.