Defining Relations on Graphs: How Hard is it in the Presence of Node Partitions?
Authors: 
M. Praveen, B. SrivathsanAuthors Info & Claims
M. Praveen, B. SrivathsanAuthors Info & ClaimsPages 159 - 172
Abstract
Designing query languages for graph structured data is an active field of research. Evaluating a query on a graph results in a relation on the set of its nodes. In other words, a query is a mechanism for defining relations on a graph. Some relations may not be definable by any query in a given language. This leads to the following question: given a graph, a query language and a relation on the graph, does there exist a query in the language that defines the relation? This is called the definability problem. When the given query language is standard regular expressions, the definability problem is known to be PSPACE-complete.
The model of graphs can be extended by labeling nodes with values from an infinite domain. These labels induce a partition on the set of nodes: two nodes are equivalent if they are labeled by the same value. Query languages can also be extended to make use of this equivalence. Two such extensions are Regular Expressions with Memory (REM) and Regular Expressions with Equality (REE).
In this paper, we study the complexity of the definability problem in this extended model when the query language is either REM or REE. We show that the definability problem is EXPSPACE-complete when the query language is REM, and it is PSPACE-complete when the query language is REE. In addition, when the query language is a union of conjunctive queries based on REM or REE, we show CoNP-completeness.
References
[1]
B. Alexe, B. T. Cate, P. G. Kolaitis, and W-C Tan. Characterizing schema mappings via data examples. ACM Trans. Database Syst., 36(4):23:1--23:48, 2011.
[2]
B. Alexe, B. T. Cate, P. G. Kolaitis, and W-C Tan. Designing and refining schema mappings via data examples. In SIGMOD, pages 133--144, 2011.
[3]
T. Antonopoulos, F. Neven, and F. Servais. Definability problems for graph query languages. In ICDT, pages 141--152, 2013.
[4]
P. Barceló. Querying graph databases. In PODS, pages 175--188, 2013.
[5]
P. Barceló, J. Pérez, and J. Reutter. Schema mappings and data exchange for graph databases. In ICDT, pages 189--200, 2013.
[6]
P. Barceló, J. Reutter, and L. Libkin. Parameterized regular expressions and their languages. Theor. Comput. Sci., 474:21--45, 2013.
[7]
D. Calvanese, G. De Giacomo, M. Lenzerini, and M. Y. Vardi. Simplifying schema mappings. In ICDT, pages 114--125, 2011.
[8]
B. T. Cate, V. Dalmau, and P. G. Kolaitis. Learning schema mappings. ACM Trans. Database Syst., 38(4):28:1--28:31, 2013.
[9]
B. T. Cate, P. G. Kolaitis, and W-C Tan. Database constraints and homomorphism dualities. In CP, pages 475--490, 2010.
[10]
A. Das Sarma, A. Parameswaran, H. Garcia-Molina, and J. Widom. Synthesizing view definitions from data. In ICDT, pages 89--103, 2010.
[11]
G.H.L. Fletcher, M. Gyssens, J. Paredaens, and D. V. Gucht. On the expressive power of the relational algebra on finite sets of relation pairs. IEEE Trans. Knowledge and Data Engg., 21(6):939--942, 2009.
[12]
A. Gheerbrant, L. Libkin, and C. Sirangelo. When is naive evaluation possible? In PODS, pages 75--86, 2013.
[13]
G. Gottlob, C. Koch, R. Baumgartner, M. Herzog, and S. Flesca. The Lixto data extraction project: Back and forth between theory and practice. In PODS, pages 1--12, 2004.
[14]
G. Gottlob and P. Senellart. Schema mapping discovery from data instances. J. ACM, 57(2):6:1--6:37, 2010.
[15]
C. Gutierrez, C. Hurtado, and A. Mendelzon. Foundations of semantic web databases. JCSS, 77(3):520--541, 2011.
[16]
M. Kaminski and N. Francez. Finite-memory automata. Theor. Comp. Sc., 134(2):329 -- 363, 1994.
[17]
E.V. Kostylev, J.L. Reutter, and D. Vrgo\vc. Containment of data graph queries. In ICDT, pages 131--142, 2014.
[18]
U. Leser. A query language for biological networks. Bioinformatics, 21(suppl 2):ii33--ii39, 2005.
[19]
L. Libkin and D. Vrgo\vc. Regular expressions for data words. In Logic for Programming, Artificial Intelligence, and Reasoning, volume 7180 of LNCS, pages 274--288. 2012.
[20]
L. Libkin and D. Vrgo\vc. Regular path queries on graphs with data. In ICDT, pages 74--85, 2012.
[21]
F. Neven, T. Schwentick, and V. Vianu. Finite state machines for strings over infinite alphabets. ACM TOCL, 5(3):403--435, 2004.
[22]
J. Pérez, M. Arenas, and C. Gutierrez. Semantics and complexity of SPARQL. ACM Trans. Database Syst., 34(3), 2009.
[23]
R. Ronen and O. Shmueli. Soql: A language for querying and creating data in social networks. In ICDE, pages 1595--1602, 2009.
[24]
H. Sakamoto and D. Ikeda. Intractability of decision problems for finite-memory automata. Theor. Comp. Sc., 231(2):297 -- 308, 2000.
[25]
P. van Emde Boas. The convenience of tilings. In Complexity, Logic and Recursion Theory, pages 331--363. Marcel Dekker Inc., 1997.
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- Defining Relations on Graphs: How Hard is it in the Presence of Node Partitions?
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Published: 20 May 2015
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