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On the complexity of join dependencies
 ACM Trans. Database Syst
, 1986
"... In [IO] a method is proposed for decomposing join dependencies (jds) in a relational database using the notion of a hinge. This method was subsequently studied in [ll] and [El. We show how the technique of decompasiti” ” can be used t ” make integrity checking m”re efficient. It turns ““t that it is ..."
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Cited by 19 (2 self)
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In [IO] a method is proposed for decomposing join dependencies (jds) in a relational database using the notion of a hinge. This method was subsequently studied in [ll] and [El. We show how the technique of decompasiti” ” can be used t ” make integrity checking m”re efficient. It turns ““t that it is important t ” find a decomposition that minimizes the “umber of edges of its largest element. We show that the decompositions obtained with the method described in (lo] are optimal in this respect. This minimality criterion leads ta the definition of the degree of cy&ity, which allows us t” classify jds and leads to the notion of ncyel*i@, of which acyclicity is a special case for n = 2. We then show that, for a fixed value of n (which may be greater than 2). integrity checking can be performed in polynomial time provided we restrict ourselves t ” ncyclic jds. Finally, we generalize a wellknown characterization for acyclic jds by proving that ncyclicity is equivalent ta “nwise consistency implies global consistency. ” As a consequence, consistency checking can be performed in polynomial time if we restrict aurselves to ncyclic jds, for a tired value of n, not necessarily equal t ” 2.
On Leaf Powers
"... For an integer k, a tree T is a kleaf root of a finite simple undirected graph G = (V, E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V, x ̸ = y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a kleaf power if it has a kleaf ..."
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Cited by 14 (2 self)
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For an integer k, a tree T is a kleaf root of a finite simple undirected graph G = (V, E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V, x ̸ = y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a kleaf power if it has a kleaf root. G is a leaf power if it is a kleaf power for some k. This notion was introduced and studied by Nishimura, Ragde and Thilikos; it has its background and motivation in computational biology and phylogeny. In this survey, we describe recent results on leaf powers, variants and generalizations. We discuss the relationship between leaf powers and strongly chordal graphs as well as fixed tolerance NeST graphs, describe some subclasses of leaf powers, give the complete inclusion structure of kleaf power classes, and describe various characterizations of 3and 4leaf powers, as well as of distancehereditary 5leaf powers. Finally we discuss two variants of the notion of kleaf power such as (k, ℓ)leaf powers and exact leaf powers, and we generalize leaf powers (of trees) to simplicial powers of graphs. Most of the presented results are part of joint work, mostly with Van Bang Le and Peter Wagner, but also with Christian Hundt, Federico Mancini, R. Sritharan, and Dieter Rautenbach.
Complexity Aspects of the Helly Property: Graphs and Hypergraphs
, 2009
"... In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. A family of subsets has the Helly property when every subfamily thereof, formed by pairwise intersecting subsets, contains a common element. Many generalizations of this property exist which are r ..."
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Cited by 7 (2 self)
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In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. A family of subsets has the Helly property when every subfamily thereof, formed by pairwise intersecting subsets, contains a common element. Many generalizations of this property exist which are relevant to some fields of mathematics, and have several applications in computer science. In this work, we survey complexity aspects of the Helly property. The main focus is on characterizations of several classes of graphs and hypergraphs related to the Helly property. We describe algorithms for solving different problems arising from the basic Helly property. We also discuss the complexity of these problems, some of them leading to NPhardness results.
A Database Interface for Mobile Computers
 In Proceedings of the 1992 Globecomm Workshop on Networking for Personal Communications Applications
, 1992
"... Computerbased personal information service is evolving beyond simple applications such as retrieval of phone numbers to include interaction with large, geographically distributed information bases. Concurrently, small, penbased, mobile computers are becoming the machine of choice for personal comp ..."
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Computerbased personal information service is evolving beyond simple applications such as retrieval of phone numbers to include interaction with large, geographically distributed information bases. Concurrently, small, penbased, mobile computers are becoming the machine of choice for personal computing. These two trends place conflicting demands on the design of database interfaces. The latter trend suggests simple interfaces that are easytouse, avoid keyboard use, and are suited for the small screens and small (relatively speaking) memory sizes of mobile machines. The former trend, however, suggests an increased sophistication in database interfaces, so as to provide access to the larger databases that are now part of a personal information service. We describe a penbased graphical database language that begins to combine these conflicting demands for simplicity and sophistication. We compare this language with previous work on graphical user interfaces designed for workstations...