Privacy-Preserving Subgraph Matching Protocol for Two Parties

Graph data structure has been widely used across many application areas, such as web data, social network, and cheminformatics. The main benefit of storing data as graphs is there exists a rich set of graph algorithms and operations that can be used to solve various computing problems, including pattern matching, data mining, and image processing. Among these graph algorithms, the subgraph isomorphism problem is one of the most fundamental algorithms that can be utilized by many higher level applications. The subgraph isomorphism problem is defined as, given two graphs [Formula: see text] and [Formula: see text], whether [Formula: see text] contains a subgraph that is isomorphic to [Formula: see text]. In this paper, we consider a special case of the subgraph isomorphism problem called the subgraph matching problem, which tests whether [Formula: see text] is a subgraph of [Formula: see text]. We propose a protocol that solve the subgraph matching problem in a privacy-preserving manner. The protocol allows two parties to jointly compute whether one graph is a subgraph of the other, while protecting the private information about the input graphs. The protocol is secure under the semi-honest setting, where each party performs the protocol faithfully.

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Permutation Pattern matching in (213, 231)-avoiding permutations

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.1329 ◽

2017 ◽

Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽

Author(s):

Both Neou ◽

Romeo Rizzi ◽

Stéphane Vialette

Keyword(s):

Pattern Matching ◽

Two Dimensional Matching

Pattern Matching Algorithms ◽

10.1093/oso/9780195113679.003.0012 ◽

1997 ◽

Author(s):

A. Amir ◽

M. Farach

Keyword(s):

Pattern Matching ◽

String Matching ◽

Higher Dimensions ◽

Natural Generalization ◽

Theoretical Problem ◽

Two Dimensional ◽

Exact Matching ◽

Matching Problem ◽

Deterministic Algorithms ◽

Special Case

String matching is a basic theoretical problem in computer science, but has been useful in implementating various text editing tasks. The explosion of multimedia requires an appropriate generalization of string matching to higher dimensions. The first natural generalization is that of seeking the occurrences of a pattern in a text where both pattern arid text are rectangles. The last few years saw a tremendous activity in two dimensional pattern matching algorithms. We naturally had to limit the amount of information that entered this chapter. We chose to concentrate on serial deterministic algorithms for some of the basic issues of two dimensional matching. Throughout this chapter we define our problems in terms of squares rather than rectangles, however, all results presented easily generalize to rectangles. The Exact Two Dimensional Matching Problem is defined as follows: . . . INPUT: Text array T[n x n] and pattern array P[m x m]. OUTPUT: All locations [i,j] in T where there is an occurrence of P, i.e. T[i+k+,j+l] = P[k+1,l+1] 0 ≤ k, l ≤ n-1. . . . A natural way of solving any generalized problem is by reducing it to a special case whose solution is known. It is therefore not surprising that most solutions to the two dimensional exact matching problem use exact string matching algorithms in one way or another. In this section, we present an algorithm for two dimensional matching which relies on reducing a matrix of characters into a one dimensional array. Let P' [1 . . .m] be a pattern which is derived from P by setting P' [i] = P[i,l]P[i,2]…P[i,m], that is, the ith character of P' is the ith row of P. Let Ti[l . . .n — m + 1], for 1 ≤ i ≤ n, be a set of arrays such that Ti[j] = T[i, j] T [ i , j + 1 ] • • • T[i, j + m-1]. Clearly, P occurs at T[i, j] iff P' occurs at Ti[j].

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Continuous matching of evolving patterns over dynamic graph data

World Wide Web ◽

10.1007/s11280-020-00860-5 ◽

2021 ◽

Author(s):

Qianzhen Zhang ◽

Deke Guo ◽

Xiang Zhao ◽

Xi Wang

Keyword(s):

Pattern Matching ◽

Wide Spectrum ◽

Dynamic Graph ◽

Matching Problem ◽

Graph Pattern Matching ◽

Graph Data ◽

Graph Pattern ◽

Matching Process ◽

Data Graph ◽

Pattern Graph

AbstractNowadays, the scale of various graphs soars rapidly, which imposes a serious challenge to develop processing and analytic algorithms. Among them, graph pattern matching is the one of the most primitive tasks that find a wide spectrum of applications, the performance of which is yet often affected by the size and dynamicity of graphs. In order to handle large dynamic graphs, incremental pattern matching is proposed to avoid re-computing matches of patterns over the entire data graph, hence reducing the matching time and improving the overall execution performance. Due to the complexity of the problem, little work has been reported so far to solve the problem, and most of them only solve the graph pattern matching problem under the scenario of the data graph varying alone. In this article, we are devoted to a more complicated but very practical graph pattern matching problem, continuous matching of evolving patterns over dynamic graph data, and the investigation presents a novel algorithm for continuously pattern matching along with changes of both pattern graph and data graph. Specifically, we propose a concise representation of partial matching solutions, which can help to avoid re-computing matches of the pattern and speed up subsequent matching process. In order to enable the updates of data graph and pattern graph, we propose an incremental maintenance strategy, to efficiently maintain the intermediate results. Moreover, we conceive an effective model for estimating step-wise cost of pattern evaluation to drive the matching process. Extensive experiments verify the superiority of .

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PRIVACY PRESERVING PATTERN MATCHING ON SEQUENCES OF EVENTS

International Journal of Computing ◽

10.47839/ijc.4.3.367 ◽

2014 ◽

pp. 85-90

Author(s):

Vladimir A. Oleshchuk

Keyword(s):

Pattern Matching ◽

Data Streams ◽

Input Sequence ◽

Privacy Preserving ◽

Matching Problem ◽

Matching Algorithm ◽

Use Pattern ◽

Pattern Matching Algorithm

We propose to use pattern matching on data streams from sensors in order to monitor and detect events of interest. We study a privacy preserving pattern matching problem where patterns are specified as sequences of constraints on input elements. We propose a new privacy preserving pattern matching algorithm over an infinite alphabet A where a pattern P is given as a sequence { pi , pi ,..., pim } 1 2 of predicates pi j defined on A . The algorithm addresses the following problem: given a pattern P and an input sequence t, find privately all positions i in t where P matches t. The privacy preserving in the context of this paper means that sensor measurements will be evaluated as predicates ( ) pi ej privately, that is, sensors will not need to disclose the measurements ( ) ( ) ( j )

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Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System

Fundamenta Informaticae ◽

10.3233/fi-2021-2002 ◽

2021 ◽

Vol 178 (3) ◽

pp. 173-185

Author(s):

Arthur Adinayev ◽

Itamar Stein

Keyword(s):

Isomorphism Problem ◽

Complete Characterization ◽

Hasse Diagram ◽

Subgraph Isomorphism ◽

Rewriting Systems ◽

Rewriting System ◽

String Rewriting ◽

Reduction Graph

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

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Multi-Fuzzy-Objective Graph Pattern Matching with Big Graph Data

Journal of Database Management ◽

10.4018/jdm.2019100102 ◽

2019 ◽

Vol 30 (4) ◽

pp. 24-40

Author(s):

Lei Li ◽

Fang Zhang ◽

Guanfeng Liu

Keyword(s):

Pattern Matching ◽

Particle Swarm Optimization Algorithm ◽

Nsga Ii ◽

Specific Domain ◽

Graph Pattern Matching ◽

Graph Data ◽

Graph Pattern ◽

Big Graph ◽

Complex Relationships ◽

Pattern Graph

Big graph data is different from traditional data and they usually contain complex relationships and multiple attributes. With the help of graph pattern matching, a pattern graph can be designed, satisfying special personal requirements and locate the subgraphs which match the required pattern. Then, how to locate a graph pattern with better attribute values in the big graph effectively and efficiently becomes a key problem to analyze and deal with big graph data, especially for a specific domain. This article introduces fuzziness into graph pattern matching. Then, a genetic algorithm, specifically an NSGA-II algorithm, and a particle swarm optimization algorithm are adopted for multi-fuzzy-objective optimization. Experimental results show that the proposed approaches outperform the existing approaches effectively.

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