Pattern Masking for Dictionary Matching: Theory and Practice

Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching ( PMDM ) problem: given...

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Published in:	Algorithmica Vol. 86; no. 6; pp. 1948 - 1978
Main Authors:	Charalampopoulos, Panagiotis, Chen, Huiping, Christen, Peter, Loukides, Grigorios, Pisanti, Nadia, Pissis, Solon P., Radoszewski, Jakub
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.06.2024 Springer Nature B.V Springer Verlag
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Bioinformatics Combinatorial analysis Computer Science Computer Systems Organization and Communication Networks Data structures Data Structures and Information Theory Dictionaries Greedy algorithms Heuristic Masking Mathematics of Computing Polynomials Queries Reduction String matching Synthetic data Theory of Computation String algorithms Dictionary matching Wildcards Record linkage Query term dropping String algorithms Dictionary matching Wildcards Record linkage
ISSN:	0178-4617, 1432-0541
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Abstract	Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching ( PMDM ) problem: given a dictionary D of d strings, each of length ℓ , a query string q of length ℓ , and a positive integer z , we are asked to compute a smallest set K ⊆ { 1 , … , ℓ } , so that if q [ i ] is replaced by a wildcard for all i ∈ K , then q matches at least z strings from D . Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k -Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial O ( ( d ℓ ) \| K \| / 3 + d ℓ ) -time and O ( d ℓ ) -space algorithm for PMDM for \| K \| = O ( 1 ) . In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k -Clique hypothesis fails (Abboud et al. in SIAM J Comput 47:2527–2555, 2018; Lincoln et al., in: 29th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018). Our combinatorial algorithm, executed with small \| K \|, is the backbone of a greedy heuristic that we propose. Our experiments on real-world and synthetic datasets show that our heuristic finds nearly-optimal solutions in practice and is also very efficient. We also generalize this algorithm for the problem of masking multiple query strings simultaneously so that every string has at least z matches in D . PMDM can be viewed as a generalization of the decision version of the dictionary matching with mismatches problem: by querying a PMDM data structure with string q and z = 1 , one obtains the minimal number of mismatches of q with any string from D . The query time or space of all known data structures for the more restricted problem of dictionary matching with at most k mismatches incurs some exponential factor with respect to k . A simple exact algorithm for PMDM runs in time O ( 2 ℓ d ) . We present a data structure for PMDM that answers queries over D in time O ( 2 ℓ / 2 ( 2 ℓ / 2 + τ ) ℓ ) and requires space O ( 2 ℓ d 2 / τ 2 + 2 ℓ / 2 d ) , for any parameter τ ∈ [ 1 , d ] . We complement our results by showing a two-way polynomial-time reduction between PMDM and the Minimum Union problem [Chlamtáč et al., ACM-SIAM Symposium on Discrete Algorithms (SODA) 2017]. This gives a polynomial-time O ( d 1 / 4 + ϵ ) -approximation algorithm for PMDM , which is tight under a plausible complexity conjecture. This is an extended version of a paper that was presented at International Symposium on Algorithms and Computation (ISAAC) 2021.
AbstractList	Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching (PMDM) problem: given a dictionary D of d strings, each of length , a query string q of length , and a positive integer z, we are asked to compute a smallest set K ⊆ {1, . . . , }, so that if q[i] is replaced by a wildcard for all i ∈ K , then q matches at least z strings from D. Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k-Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial O((d ) \|K \|/3 + d )-time and O(d )-space algorithm for PMDM for \|K \| = O(1). In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k-Clique hypothesis fails ( Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching (PMDM) problem: given a dictionary D of d strings, each of length ℓ, a query string q of length ℓ, and a positive integer z, we are asked to compute a smallest set K⊆{1,…,ℓ}, so that if q[i] is replaced by a wildcard for all i∈K, then q matches at least z strings from D. Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k-Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial O((dℓ)\|K\|/3+dℓ)-time and O(dℓ)-space algorithm for PMDM for \|K\|=O(1). In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k-Clique hypothesis fails (Abboud et al. in SIAM J Comput 47:2527–2555, 2018; Lincoln et al., in: 29th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018). Our combinatorial algorithm, executed with small \|K\|, is the backbone of a greedy heuristic that we propose. Our experiments on real-world and synthetic datasets show that our heuristic finds nearly-optimal solutions in practice and is also very efficient. We also generalize this algorithm for the problem of masking multiple query strings simultaneously so that every string has at least z matches in D. PMDM can be viewed as a generalization of the decision version of the dictionary matching with mismatches problem: by querying a PMDM data structure with string q and z=1, one obtains the minimal number of mismatches of q with any string from D. The query time or space of all known data structures for the more restricted problem of dictionary matching with at most k mismatches incurs some exponential factor with respect to k. A simple exact algorithm for PMDM runs in time O(2ℓd). We present a data structure for PMDM that answers queries over D in time O(2ℓ/2(2ℓ/2+τ)ℓ) and requires space O(2ℓd2/τ2+2ℓ/2d), for any parameter τ∈[1,d]. We complement our results by showing a two-way polynomial-time reduction between PMDM and the Minimum Union problem [Chlamtáč et al., ACM-SIAM Symposium on Discrete Algorithms (SODA) 2017]. This gives a polynomial-time O(d1/4+ϵ)-approximation algorithm for PMDM, which is tight under a plausible complexity conjecture. This is an extended version of a paper that was presented at International Symposium on Algorithms and Computation (ISAAC) 2021. Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching ( PMDM ) problem: given a dictionary D of d strings, each of length ℓ , a query string q of length ℓ , and a positive integer z , we are asked to compute a smallest set K ⊆ { 1 , … , ℓ } , so that if q [ i ] is replaced by a wildcard for all i ∈ K , then q matches at least z strings from D . Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k -Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial O ( ( d ℓ ) \| K \| / 3 + d ℓ ) -time and O ( d ℓ ) -space algorithm for PMDM for \| K \| = O ( 1 ) . In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k -Clique hypothesis fails (Abboud et al. in SIAM J Comput 47:2527–2555, 2018; Lincoln et al., in: 29th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018). Our combinatorial algorithm, executed with small \| K \|, is the backbone of a greedy heuristic that we propose. Our experiments on real-world and synthetic datasets show that our heuristic finds nearly-optimal solutions in practice and is also very efficient. We also generalize this algorithm for the problem of masking multiple query strings simultaneously so that every string has at least z matches in D . PMDM can be viewed as a generalization of the decision version of the dictionary matching with mismatches problem: by querying a PMDM data structure with string q and z = 1 , one obtains the minimal number of mismatches of q with any string from D . The query time or space of all known data structures for the more restricted problem of dictionary matching with at most k mismatches incurs some exponential factor with respect to k . A simple exact algorithm for PMDM runs in time O ( 2 ℓ d ) . We present a data structure for PMDM that answers queries over D in time O ( 2 ℓ / 2 ( 2 ℓ / 2 + τ ) ℓ ) and requires space O ( 2 ℓ d 2 / τ 2 + 2 ℓ / 2 d ) , for any parameter τ ∈ [ 1 , d ] . We complement our results by showing a two-way polynomial-time reduction between PMDM and the Minimum Union problem [Chlamtáč et al., ACM-SIAM Symposium on Discrete Algorithms (SODA) 2017]. This gives a polynomial-time O ( d 1 / 4 + ϵ ) -approximation algorithm for PMDM , which is tight under a plausible complexity conjecture. This is an extended version of a paper that was presented at International Symposium on Algorithms and Computation (ISAAC) 2021. Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application areas, such as in record linkage of personal data. This work formalizes the Pattern Masking for Dictionary Matching ( PMDM ) problem: given a dictionary $$\mathscr {D}$$ D of d strings, each of length $$\ell $$ ℓ , a query string q of length $$\ell $$ ℓ , and a positive integer z , we are asked to compute a smallest set $$K\subseteq \{1,\ldots ,\ell \}$$ K ⊆ { 1 , … , ℓ } , so that if q [ i ] is replaced by a wildcard for all $$i\in K$$ i ∈ K , then q matches at least z strings from $$\mathscr {D}$$ D . Solving PMDM allows providing data utility guarantees as opposed to existing approaches. We first show, through a reduction from the well-known k -Clique problem, that a decision version of the PMDM problem is NP-complete, even for binary strings. We thus approach the problem from a more practical perspective. We show a combinatorial $$\mathscr {O}((d\ell )^{\|K\|/3}+d\ell )$$ O ( ( d ℓ ) \| K \| / 3 + d ℓ ) -time and $$\mathscr {O}(d\ell )$$ O ( d ℓ ) -space algorithm for PMDM for $$\|K\|=\mathscr {O}(1)$$ \| K \| = O ( 1 ) . In fact, we show that we cannot hope for a faster combinatorial algorithm, unless the combinatorial k -Clique hypothesis fails (Abboud et al. in SIAM J Comput 47:2527–2555, 2018; Lincoln et al., in: 29th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018). Our combinatorial algorithm, executed with small \| K \|, is the backbone of a greedy heuristic that we propose. Our experiments on real-world and synthetic datasets show that our heuristic finds nearly-optimal solutions in practice and is also very efficient. We also generalize this algorithm for the problem of masking multiple query strings simultaneously so that every string has at least z matches in $$\mathscr {D}$$ D . PMDM can be viewed as a generalization of the decision version of the dictionary matching with mismatches problem: by querying a PMDM data structure with string q and $$z=1$$ z = 1 , one obtains the minimal number of mismatches of q with any string from $$\mathscr {D}$$ D . The query time or space of all known data structures for the more restricted problem of dictionary matching with at most k mismatches incurs some exponential factor with respect to k . A simple exact algorithm for PMDM runs in time $$\mathscr {O}(2^\ell d)$$ O ( 2 ℓ d ) . We present a data structure for PMDM that answers queries over $$\mathscr {D}$$ D in time $$\mathscr {O}(2^{\ell /2}(2^{\ell /2}+\tau )\ell )$$ O ( 2 ℓ / 2 ( 2 ℓ / 2 + τ ) ℓ ) and requires space $$\mathscr {O}(2^{\ell }d^2/\tau ^2+2^{\ell /2}d)$$ O ( 2 ℓ d 2 / τ 2 + 2 ℓ / 2 d ) , for any parameter $$\tau \in [1,d]$$ τ ∈ [ 1 , d ] . We complement our results by showing a two-way polynomial-time reduction between PMDM and the Minimum Union problem [Chlamtáč et al., ACM-SIAM Symposium on Discrete Algorithms (SODA) 2017]. This gives a polynomial-time $$\mathscr {O}(d^{1/4+\epsilon })$$ O ( d 1 / 4 + ϵ ) -approximation algorithm for PMDM , which is tight under a plausible complexity conjecture. This is an extended version of a paper that was presented at International Symposium on Algorithms and Computation (ISAAC) 2021.
Author	Pissis, Solon P. Radoszewski, Jakub Chen, Huiping Christen, Peter Charalampopoulos, Panagiotis Loukides, Grigorios Pisanti, Nadia
Author_xml	– sequence: 1 givenname: Panagiotis surname: Charalampopoulos fullname: Charalampopoulos, Panagiotis organization: School of Computing and Mathematical Sciences, Birkbeck, University of London – sequence: 2 givenname: Huiping surname: Chen fullname: Chen, Huiping email: h.chen.13@bham.ac.uk organization: School of Computer Science, University of Birmingham – sequence: 3 givenname: Peter surname: Christen fullname: Christen, Peter organization: Australian National University – sequence: 4 givenname: Grigorios surname: Loukides fullname: Loukides, Grigorios organization: Department of Informatics, King’s College London – sequence: 5 givenname: Nadia surname: Pisanti fullname: Pisanti, Nadia organization: Università di Pisa – sequence: 6 givenname: Solon P. orcidid: 0000-0002-1445-1932 surname: Pissis fullname: Pissis, Solon P. email: solon.pissis@cwi.nl organization: CWI, Vrije Universiteit – sequence: 7 givenname: Jakub surname: Radoszewski fullname: Radoszewski, Jakub organization: Institute of Informatics, University of Warsaw
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Snippet	Data masking is a common technique for sanitizing sensitive data maintained in database systems which is becoming increasingly important in various application...
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Bioinformatics Combinatorial analysis Computer Science Computer Systems Organization and Communication Networks Data structures Data Structures and Information Theory Dictionaries Greedy algorithms Heuristic Masking Mathematics of Computing Polynomials Queries Reduction String matching Synthetic data Theory of Computation
Title	Pattern Masking for Dictionary Matching: Theory and Practice
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