Tree Centroid Properties Clarification

Multi-way graph partition by stochastic probe

Graph matching, set covering and partitioning problems are both theoretically and practically important in decision support systems. Numerous situations have been modeled as graph matching, set covering and partitioning problems. These situations include applications in the areas of task assignment, marriage problem, airline crew scheduling, truck deliveries or vehicle routing, political redistricting, etc. Relational database systems currently support these applications merely by providing some programming languages which are used to write the programs associated with the data. These programming languages are complete as opposed to existing query languages like SQL. These languages, since they are complete, have the usual complexity of a powerful language and lack the simplicity of query languages. This increases application development effort. Relational operators and the query language SQL are extended in this present work in order to enable these problems to be stated and solved directly by the relational database systems leading to benefits of improved data independence, increased productivity, and better performance. The relational operators are extended with six operators, i.e., match, maxmatch, cover, mincover, partition, and minpartition. Properties of these operators are described. Some of these operators may possibly take a very long time in finding a solution. Genetic algorithms are proposed. These algorithms are bounded by a polynomial time. These algorithms therefore enable DBMS to be capable of responding to queries involving proposed operators in a given time constraint. The database operations and query languages extended in this research provide a powerful tool for users as a database‐query tool which supports some decision support systems for information retrieval from a database.

With the rapid expansion of social networks, efficiently mining and analyzing massive graph data has become a fundamental challenge in social network research. Graph partitioning plays a pivotal role in enhancing the performance of such analyses. However, conventional graph partitioning methods predominantly rely on local structural information and often overlook the rich attribute information associated with vertices in social network graphs. To overcome this limitation, this paper introduces GP-DQN (Graph Partitioning via Double Deep Q-Network), a large-scale graph partitioning algorithm that jointly considers structural correlations, attribute disparities among user vertices, and partition load balancing. GP-DQN encodes partition load metrics and vertex attributes into vector representations and employs a Graph Convolutional Network (GCN) to aggregate both vertex features and neighborhood structures, thereby improving the accuracy and scalability of the partitioning process. A tailored reward function is designed to guide partitioning actions, where a Double Deep Q-Network (DDQN) predicts the expected partitioning rewards based on GCN-extracted features for assigning each vertex to different partitions. The partitioning strategy is iteratively optimized using both immediate and expected rewards, ultimately achieving balanced load distribution while minimizing the number of edge cuts. Experimental results demonstrate that GP-DQN produces well-balanced partitions with significantly fewer edge cuts, leading to enhanced computational efficiency within each partition.

String matching is an algorithm for matching a text to another text or also known as a text search. There are several algorithms that can be used for string matching, including the Boyer-Moore algorithm and the Brute Force algorithm. The Boyer-Moore algorithm is a string matching algorithm published by Robert S. Boyer and J. Strother Moore in 1977. This algorithm is considered the most efficient algorithm in general applications. The Boyer-Moore algorithm starts matching characters from the pattern on the right. While the Brute Force algorithm is an algorithm that matches a pattern with all text between 0 and n-m to find the existence of a pattern in the text. These two algorithms have different patterns in the search process. In this article, a comparative analysis of the performance of the Boyer-Moore and Brute Force algorithms is carried out in a case study of the search for the Big Indonesian Dictionary (KBBI) based on Android. The search process is carried out by searching based on words and word descriptions. The results of this study indicate that the criteria for running time, the Brute Force algorithm is faster than the Boyer-Moore algorithm with the total running time of the Brute Force algorithm is 168.3 ms in words, 6994.16 ms in word descriptions, while the Boyer-Moore algorithm for running time reached 304.7 ms on the word, 8654.77 ms on the word description. In the testing criteria based on related keywords, the two algorithms can display the same list of related keywords.

We propose a heuristic for parallel partitioning of graphs into equi-sized components. In particular, we identify a relationship between the graph partitioning problem (GPP) and the traveling saleman problem (TSP), and use that to reduce partitioning to TSP. Given that better performing heuristics are known for TSP than are for GPP, this reduction also leads to improved GPP heuristics. What is more, a good GPP solution can also be used to speed up computation of TSP.We first derive a good bi-partition from a cut of the TSP cycle in time proportional to the number of edges in the graph. We then continue this bi-partitioning recursively until the required number of partitions are left. Further, in order to speed up the computation of TSP, which we use as a subroutine, we perform an initial rough partitioning of the graph into K parts, compute TSP tours in each of these smaller partitions and then merge these local tours to solve the full TSP.We then use this full TSP solution to obtain the final partitioning in parallel. Our empirical analysis shows that for partition count k ≥ 32, our parallel algorithm gives a cut better in size than that of algorithms known for low cut-size (e.g., KaBaPE), and when time is of concern, it finishes in significantly less time with comparable cuts. We also show that our algorithm gives much smaller cuts in comparable time than those known for fast computation (e.g., PT-Scotch).

This presentation explores parallel computing dynamics and its application in materials science.

We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local nature of the connectivity condition usually results in very challenging algorithmic tasks. The balanced crown decomposition is a combination of a crown decomposition and a balanced partition which makes it applicable to graph editing as well as graph packing and partitioning problems. We illustrate this by deriving improved approximation algorithms and kernelization for a variety of such problems. In particular, through this structure, we obtain the first constant-factor approximation for the Balanced Connected Partition (BCP) problem, where the task is to partition a vertex-weighted graph into k connected components of approximately equal weight. We derive a 3-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component.

In the manual dictionary the more words are accommodated, the heavier the dictionary. Dictionaries that are generally book-shaped are difficult to carry anywhere because they are thick and heavy. With this mobile-based computer dictionary application, users no longer need to carry heavy dictionaries and the search process will also be faster and easier. This mobile-based kmputer dictionary application is created using the java programming language with the NetBeans 7.0 editor and using an RMS (Record Management System) based database. So it can be installed on various types of mobile phones that already support Java. String Matching is one of the algorithms used to speed up the search process for the desired word. String matching algorithms have been used frequently before as examples in the process of matching strings based on the equation of text data namely Brute Force. Because this Brute Force algorithm can be used to perform string or text searches. Brute force algorithm is an algorithm to match a pattern with all text between 0 and n-m to find the presence of a pattern in text.

Partitioning approach oriented to the decentralised predictive control of large-scale systems

Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing execution on multiprocessor architectures under hardware resource constraints. However due to program memory restrictions in embedded multiprocessor systems, applications need to be divided into parts without cyclic dependencies. We found that this can be done by a subsequent second graph partitioning step with an additional acyclicity constraint. We have four main contributions. First, we show that this more constrained version of the graph partitioning problem is NP-complete and present linear time heuristics. We then integrate them into an existing multi-level graph partitioning framework to better handle large graphs. This achieves a 9% reduction of the edge cut compared to the previous single-level algorithm. Based on this, we engineer an evolutionary algorithm to further reduce the cut, achieving a 30% reduction on average compared to the state of the art. Finally, we integrate the partitioning heuristics into a graph compiler for an embedded multiprocessor architecture and show that this can reduce the amount of communication for a real-world imaging application and thereby accelerate it by an average of 11%. It is shown that the compiler can emit optimized code for vastly different hardware platforms using the heuristics. In addition, we demonstrate how a custom fitness function for the evolutionary algorithm can be used to optimize other objectives like load balancing if the communication volume is not predominantly important on a given hardware platform.

k-way graph partitioning is an NP-complete problem, which is applied to various tasks such as route planning, image segmentation, community detection, and high-performance computing. The approximate methods constitute a useful solution for these types of problems. Thus, many research studies have focused on developing meta-heuristic algorithms to tackle the graph partitioning problem. Local search is one of the earliest methods that has been applied efficiently to this type of problem. Recent studies have explored various types of local search methods and have improved them such that they can be used with the partitioning process. Moreover, local search methods are widely integrated with population-based approaches, to provide the best diversification and intensification for the problem space. This study emphasizes the local search approaches, as well as their combination with other graph partitioning approaches. At present, none of the surveys in the literature has focused on this class of state of the art approaches in much detail. In this study, the vital parts of these approaches including neighborhood structure, acceptance criterion, and the ways of combining them with other approaches, are highlighted. Additionally, we provide an experimental comparison that shows the variance in the performance of the reviewed methods. Hence, this study clarifies these methods to show their advantages and limitations for the targeted problem, and thus can aid in the direction of research flow towards the area of graph partitioning.

Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wish to partition G into connected components by deleting edges from G so that the total weight of each component is at least l and at most u. Such an “almost uniform” partition is called an $(l, u) \mbox{-}$partition. We deal with three problems to find an $(l, u) \mbox{-}$partition of a given graph. The minimum partition problem is to find an $(l, u) \mbox{-}$partition with the minimum number of components. The maximum partition problem is defined similarly. The p-partition problem is to find an $(l, u) \mbox{-}$partition with a fixed number p of components. All these problems are NP-complete or NP-hard even for series-parallel graphs. In this paper we show that both the minimum partition problem and the maximum partition problem can be solved in time O(u4n) and the p-partition problem can be solved in time O(p2u4n) for any series-parallel graph of n vertices. The algorithms can be easily extended for partial k-trees, that is, graphs with bounded tree-width.

We propose a new crossover that generalizes cycle crossover to permutations with repetitions and naturally suits partition problems. We tested it on graph partitioning problems obtaining excellent results.

The Covid-19 pandemic has started to subside. However, after the pandemic subsided the obesity rate in Indonesia continued to increase. The new habits formed after the pandemic are activities that can be done at home. This is an opportunity to be able to reduce obesity by doing physical activity at home. Physical activity undertaken specifically to lose weight. However, various problems arise when doing physical activity. Such as requiring expensive fees, monotony, and others. Mobile exergame is one solution to this problem. In previous research, exergames that use the brute force algorithm in determining physical activity take a long time. This problem will be solved using a greedy algorithm which also uses a maximum profit strategy. Descriptive statistics are used to compare the average time needed by the two algorithms to select the physical activity to be performed in an exergame. The results of this study indicate that in terms of time the greedy algorithm that uses the maximum profit strategy is proven to be faster than the brute force algorithm.

The m‐way graph partitioning problem is of central importance in combinatorial optimization. It has many important applications in fields such as VLSI circuit design, task allocation in distributed computing systems, and network partitioning. In this paper, we propose an efficient genetic algorithm to solve this problem. The proposed method searches a large solution space and finds the best possible solution by adjusting the intensification and diversification automatically during the optimization process. The proposed method is tested on a large number of instances and compared with some existing algorithms. The experimental results show that the proposed algorithm is superior to its competitors in terms of computation time and solution quality. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.