Reverse search for enumeration

Avis, David; Fukuda, Komei

doi:10.1016/0166-218x(95)00026-n

Cited by 605 publications

(590 citation statements)

References 10 publications

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“…In fact, enumerating all objects that satisfy a specified property is a fundamental problem not only in data mining but also in a lot of other fields such as combinatorics, computational geometry, and operations research. Avis and Fukuda (1996) presented an exhaustive search technique, called reverse search, in a general framework which includes various enumeration problems in broader applications. In reverse search, we first define a rooted spanning tree, called enumeration tree, in which nodes are the set to be enumerated.…”

Section: Reverse Search Reformulation For Enumerating Frequent Subgraphsmentioning

confidence: 99%

“…Our algorithm is closely related with those for mining closed frequent subgraphs (by depth-first search (DFS) (Yan and Han 2003) and by breadth-first search (BFS) (Borgelt et al 2004)), which however sometimes have serious flaws on the completeness of enumerating all closed frequent graphs due to overpruning (Wörlein 2006;Borgelt and Meinl 2006). Thus, in this work, to avoid the problem of overpruning, we started with formulating the problem of mining frequent subgraphs by using a general enumeration (or pattern growth) framework called "reverse-search" (Avis and Fukuda 1996), for which the completeness of enumeration is guaranteed. We emphasize that this formulation makes the completeness and the uniqueness of frequent subgraphs clear not only in our problem but in more general subgraph enumeration from a given graph dataset.…”

Section: Introductionmentioning

confidence: 99%

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Efficiently mining δ-tolerance closed frequent subgraphs

Takigawa

Mamitsuka

2010

Mach Learn

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The output of frequent pattern mining is a huge number of frequent patterns, which are very redundant, causing a serious problem in understandability. We focus on mining frequent subgraphs for which well-considered approaches to reduce the redundancy are limited because of the complex nature of graphs. Two known, standard solutions are closed and maximal frequent subgraphs, but closed frequent subgraphs are still redundant and maximal frequent subgraphs are too specific. A more promising solution is δ-tolerance closed frequent subgraphs, which decrease monotonically in δ, being equal to maximal frequent subgraphs and closed frequent subgraphs for δ = 0 and 1, respectively. However, the current algorithm for mining δ-tolerance closed frequent subgraphs is a naive, two-step approach in which frequent subgraphs are all enumerated and then sifted according to δ-tolerance closedness. We propose an efficient algorithm based on the idea of "reverse-search" by which the completeness of enumeration is guaranteed and for which new pruning conditions are incorporated. We empirically demonstrate that our approach significantly reduced the amount of real computation time of two compared algorithms for mining δ-tolerance closed frequent subgraphs, being pronounced more for practical settings.

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Section: Reverse Search Reformulation For Enumerating Frequent Subgraphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficiently mining δ-tolerance closed frequent subgraphs

Takigawa

Mamitsuka

2010

Mach Learn

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“…Obviously, we can express the zonotope Z as a polytope, and then compute the intersection between the polytope and the hyperplane G. The good news is that computing a H-representation [14] of a zonotope can be done polynomially in the number of its facets [15], the bad news is that a zonotope with r generators in dimension d might have up to 2 r d−1 facets [16]. Even for relatively small zonotopes, this can be prohibitively large.…”

Section: Intersection Of a Zonotope And A Hyperplanementioning

confidence: 99%

Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis

Girard

Guernic

2008

Hybrid Systems: Computation and Control

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Abstract. In this paper, we are concerned with the problem of computing the reachable sets of hybrid systems with (possibly high dimensional) linear continuous dynamics and guards defined by switching hyperplanes. For the reachability analysis of the continuous dynamics, we use an efficient approximation algorithm based on zonotopes. In order to use this technique for the analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e. scalable and accurate) way. For that purpose, we need to approximate the intersection of the continuous reachable sets with the guards enabling the discrete transitions. The main contribution of this paper is a novel algorithm for computing efficiently a tight over-approximation of the intersection of (possibly high-order) zonotopes with a hyperplane. We show the accuracy and the scalability of our approach by considering two examples of reachability analysis of hybrid systems.

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“…Học viện Bưu chính Viễn thông 4 Viện Cơ học và Tin học ứng dụng 5 Trường Đại học Tây Bắc 1 hoangquang@ioit.ac.vn, 2 vdthi@vnu.edu.vn, 4 tuyetdv@gmail.com, 5 kienptr@gmail.com…”

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