Takeaki Uno

New Algorithms for Enumerating All Maximal Cliques

In this paper, we consider the problems of generating all maximal (bipartite) cliques in a given (bipartite) graph G=(V,E) with n vertices and m edges. We propose two algorithms for enumerating all maximal cliques. One runs with O(M(n)) time delay and in O(n 2) space and the other runs with O(Δ4) time delay and in O(n+m) space, where Δ denotes the maximum degree of G, M(n) denotes the time needed to multiply two n × n matrices, and the latter one requires O(nm) time as a preprocessing.

An Efficient Algorithm for Enumerating Closed Patterns in Transaction Databases

The class of closed patterns is a well known condensed representations of frequent patterns, and have recently attracted considerable interest. In this paper, we propose an efficient algorithm LCM (Linear time Closed pattern Miner) for mining frequent closed patterns from large transaction databases. The main theoretical contribution is our proposed prefix-preserving closure extension of closed patterns, which enables us to search all frequent closed patterns in a depth-first manner, in linear time for the number of frequent closed patterns. Our algorithm do not need any storage space for the previously obtained patterns, while the existing algorithms needs it. Performance comparisons of LCM with straightforward algorithms demonstrate the advantages of our prefix-preserving closure extension.

Fast Algorithms to Enumerate All Common Intervals of Two Permutations

Abstract. Given two permutations of n elements, a pair of intervals of these permutations consisting of the same set of elements is called a commoninterval . Some genetic algorithms based on such common intervals have been proposed for sequencing problems and have exhibited good prospects. In this paper we propose three types of fast algorithms to enumerate all common intervals: (i) a simple O(n2) time algorithm (LHP), whose expected running time becomes O(n) for two randomly generated permutations, (ii) a practically fast O(n2) time algorithm (MNG) using the reverse Monge property, and (iii) an O(n+K) time algorithm (RC), where K

Effective Local Search Algorithms for Routing and Scheduling Problems with General Time-Window Constraints

(\leq {n \choose 2})

LCM ver.3: collaboration of array, bitmap and prefix tree for frequent itemset mining

is the number of common intervals. It will also be shown that the expected number of common intervals for two random permutations is O(1) . This result gives a reason for the phenomenon that the expected time complexity O(n) of the algorithm LHP is independent of K . Among the proposed algorithms, RC is most desirable from the theoretical point of view; however, it is quite complicated compared with LHP and MNG. Therefore, it is possible that RC is slower than the other two algorithms in some cases. For this reason, computational experiments for various types of problems with up to n=106 are conducted. The results indicate that (i) LHP and MNG are much faster than RC for two randomly generated permutations, and (ii) MNG is rather slower than LHP for random inputs; however, there are cases in which LHP requires Ω(n2) time, but MNG runs in o(n2) time and is faster than both LHP and RC.

Weighted Substructure Mining for Image Analysis

We propose local search algorithms for the vehicle routing problem with soft time-window constraints. The time-window constraint for each customer is treated as a penalty function, which is very general in the sense that it can be nonconvex and discontinuous as long as it is piecewise linear. In our algorithm, we use local search to assign customers to vehicles and to find orders of customers for vehicles to visit. Our algorithm employs an advanced neighborhood, called the cyclic-exchange neighborhood, in addition to standard neighborhoods for the vehicle routing problem. After fixing the order of customers for a vehicle to visit, we must determine the optimal start times of processing at customers so that the total penalty is minimized. We show that this problem can be efficiently solved by using dynamic programming, which is then incorporated in our algorithm. We report computational results for various benchmark instances of the vehicle routing problem. The generality of time-window constraints allows us to handle a wide variety of scheduling problems. As an example, we mention in this paper an application to a production scheduling problem with inventory cost, and report computational results for real-world instances.

Enumeration of condition-dependent dense modules in protein interaction networks

For a transaction database, a frequent itemset is an itemset included in at least a specified number of transactions. To find all the frequent itemsets, the heaviest task is the computation of frequency of each candidate itemset. In the previous studies, there are roughly three data structures and algorithms for the computation: bitmap, prefix tree, and array lists. Each of these has its own advantage and disadvantage with respect to the density of the input database. In this paper, we propose an efficient way to combine these three data structures so that in any case the combination gives the best performance.

Algorithms for Enumerating All Perfect, Maximum and Maximal Matchings in Bipartite Graphs

In Web-related applications of image categorization, it is desirable to derive an interpretable classification rule with high accuracy. Using the bag-of-words representation and the linear support vector machine, one can partly fulfill the goal, but the accuracy of linear classifiers is not high and the obtained features are not informative for users. We propose to combine item set mining and large margin classifiers to select features from the power set of all visual words. Our resulting classification rule is easier to browse and simpler to understand, because each feature has richer information. As a next step, each image is represented as a graph where nodes correspond to local image features and edges encode geometric relations between features. Combining graph mining and boosting, we can obtain a classification rule based on subgraph features that contain more information than the set features. We evaluate our algorithm in a web-retrieval ranking task where the goal is to reject outliers from a set of images returned for a keyword query. Furthermore, it is evaluated on the supervised classification tasks with the challenging VOC2005 data set. Our approach yields excellent accuracy in the unsupervised ranking task compared to a recently proposed probabilistic model and competitive results in the supervised classification task.

An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

We developed a new method to search protein networks functionally similar to a given query signal transduction pathway within protein interaction networks. This method consists of two parts: 1) a backtracking search algorithm to find topologically identical subgraphs and 2) a measurement of similarity between proteins by using Gene Ontology [1]. For validation of our method, we implemented a software tool and compared its performance with that of PathBLAST [2] on the search of MAPK signal transduction cascades [3]. The result showed that our software tool has equal or better performance than that of PathBLAST.

An Efficient Algorithm for Solving Pseudo Clique Enumeration Problem

For a bipartite graph G = (V, E), (1) perfect, (2) maximum and (3) maximal matchings are matchings (1) such that all vertices are incident to some matching edges, (2) whose cardinalities are maximum among all matchings, (3) which are contained in no other matching. In this paper, we present three algorithms for enumerating these three types of matchings. Their time complexities are O(|V |) per a matching.