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28
Directed Hypergraphs And Applications
, 1992
"... We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorith ..."
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Cited by 141 (5 self)
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We deal with directed hypergraphs as a tool to model and solve some classes of problems arising in Operations Research and in Computer Science. Concepts such as connectivity, paths and cuts are defined. An extension of the main duality results to a special class of hypergraphs is presented. Algorithms to perform visits of hypergraphs and to find optimal paths are studied in detail. Some applications arising in propositional logic, AndOr graphs, relational data bases and transportation analysis are presented. January 1990 Revised, October 1992 ( * ) This research has been supported in part by the "Comitato Nazionale Scienza e Tecnologia dell'Informazione", National Research Council of Italy, under Grant n.89.00208.12, and in part by research grants from the National Research Council of Canada. 1 Dipartimento di Informatica, Università di Pisa, Italy 2 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada 2 INTRODUCTION Hypergraphs, a generaliz...
Optimal Traversal of Directed Hypergraphs
, 1992
"... A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. Directed hypergraphs are used in several contexts to model different combinatorial structures, such as functional dependencies [Ull82], Horn clauses in proposi ..."
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Cited by 35 (2 self)
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A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. Directed hypergraphs are used in several contexts to model different combinatorial structures, such as functional dependencies [Ull82], Horn clauses in propositional calculus [AI91], ANDOR graphs [Nil82], Petri nets [Pet62]. A hyperpath, similarly to the notion of path in directed graphs, consists of a connection among nodes using hyperarcs. Unlike paths in graphs, hyperpaths are suitable of different definitions of measure, corresponding to different concepts arising in various applications. In this paper we consider the problem of finding minimal hyperpaths according to several measures. We show that some of these problems are, not surprisingly, NPhard. However, if the measure function on hyperpaths matches certain conditions (which we define as valuebased measure functions) , the problem turns out to be solvable in polynomial time. We...
SCHEDULING WITH AND/OR PRECEDENCE CONSTRAINTS
, 2004
"... In many scheduling applications it is required that the processing of some job be postponed until some other job, which can be chosen from a pregiven set of alternatives, has been completed. The traditional concept of precedence constraints fails to model such restrictions. Therefore, the concept h ..."
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Cited by 30 (1 self)
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In many scheduling applications it is required that the processing of some job be postponed until some other job, which can be chosen from a pregiven set of alternatives, has been completed. The traditional concept of precedence constraints fails to model such restrictions. Therefore, the concept has been generalized to socalled and/or precedence constraints which can cope with this kind of requirement. In the context of traditional precedence constraints, feasibility, transitivity, and the computation of earliest start times for jobs are fundamental, wellstudied problems. The purpose of this paper is to provide efficient algorithms for these tasks for the more general model of and/or precedence constraints. We show that feasibility as well as many questions related to transitivity can be solved by applying essentially the same lineartime algorithm. In order to compute earliest start times we propose two polynomialtime algorithms to cope with different classes of time distances between jobs.
Schema versioning in data warehouses: enabling crossversion querying via schema augmentation
 IN DATA & KNOWLEDGE ENGINEERING
, 2006
"... As several mature implementations of data warehousing systems are fully operational, a crucial role in preserving their uptodateness is played by the ability to manage the changes that the data warehouse (DW) schema undergoes over time in response to evolving business requirements. In this paper w ..."
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Cited by 16 (3 self)
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As several mature implementations of data warehousing systems are fully operational, a crucial role in preserving their uptodateness is played by the ability to manage the changes that the data warehouse (DW) schema undergoes over time in response to evolving business requirements. In this paper we propose an approach to schema versioning in DWs, where the designer may decide to undertake some actions on old data aimed at increasing the flexibility in formulating crossversion queries, i.e., queries spanning multiple schema versions. First, we introduce a representation of DW schemata as graphs of simple functional dependencies, and discuss its properties. Then, after defining an algebra of schema graph modification operations aimed at creating new schema versions, we discuss how augmented schemata can be introduced to increase flexibility in crossversion querying. Next, we show how a history of versions for DW schemata is managed and discuss the relationship between the temporal horizon spanned by a query and the schema on which it can consistently be formulated.
An Efficient Algorithm to Compute the Candidate Keys of a Relational Database Schema
, 1996
"... We provide an efficient algorithm for computing the candidate keys of a relational database schema. The algorithm exploits the ‘arrangement’ of attributes in the functional dependencies to determine which attributes are essential and useful for determining the keys and which attributes should not be ..."
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Cited by 7 (0 self)
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We provide an efficient algorithm for computing the candidate keys of a relational database schema. The algorithm exploits the ‘arrangement’ of attributes in the functional dependencies to determine which attributes are essential and useful for determining the keys and which attributes should not be considered. A more generalized algorithm using attribute graphs is then provided which allows a uniform and simplified solution to find all possible keys of a relational database schema when the attribute graph of Functional Dependencies (FDs) is not strongly connected.
Hypergraph Traversal Revisited: Cost Measures and Dynamic Algorithms
 Lecture Notes in Computer Science
, 1998
"... . Directed hypergraphs are used in several applications to model different combinatorial structures. A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. A hyperpath, similarly to the notion of path in directed ..."
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Cited by 6 (0 self)
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. Directed hypergraphs are used in several applications to model different combinatorial structures. A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. A hyperpath, similarly to the notion of path in directed graphs, consists of a connection among nodes using hyperarcs. Unlike paths in graphs, however, hyperpaths are suitable of many different definitions of measure, corresponding to different concepts arising in various applications. In this paper we consider the problem of finding optimal hyperpaths according to several measures. We also provide results that may shed some light on the intrinsic complexity of finding optimal hyperpaths. 1 Introduction A directed hypergraph is a generalization of the concept of directed graph. It was first introduced in [2] to represent functional dependencies in relational data base schemata. While directed graphs are normally used for representing onet...
On the complexity of strongly connected components in directed hypergraphs
 Algorithmica
"... Abstract. We study the problem of determining strongly connected components (Sccs) of directed hypergraphs. The main contribution is an algorithm computing the terminal strongly connected components (i.e. Sccs which do not reach any other components than themselves). The time complexity of the algo ..."
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Cited by 6 (0 self)
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Abstract. We study the problem of determining strongly connected components (Sccs) of directed hypergraphs. The main contribution is an algorithm computing the terminal strongly connected components (i.e. Sccs which do not reach any other components than themselves). The time complexity of the algorithm is almost linear, which is a significant improvement over the known methods which are quadratic time. This also proves that the problems of (i) testing strong connectivity, (ii) and determining the existence of a sink, can be both solved in almost linear time in directed hypergraphs. We also highlight an important discrepancy between the reachability relations in directed hypergraphs and graphs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. We also prove linear time reductions from combinatorial problems on the subset partial order, in particular from the wellstudied problem of finding all minimal sets among a given family, to the problem of computing the Sccs in directed hypergraphs. 1.
Linear Connectivity Problems in Directed Hypergraphs
"... We introduce a notion of hyperconnection (formally denoted Lhyperpath) between nodes in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs. We show that some interesting questions in problem domains such as secret transfer protocols and routing in ..."
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Cited by 5 (0 self)
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We introduce a notion of hyperconnection (formally denoted Lhyperpath) between nodes in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs. We show that some interesting questions in problem domains such as secret transfer protocols and routing in packet filtered networks are basically questions about the existence of Lhyperpaths in directed hypergraphs. We study the computational complexity of problems related to Lhyperpaths and the Lcyclomatic number of directed hypergraphs (the minimum number of hyperedges that need to be deleted to make a directed hypergraph free of Lhypercycles). We prove that the Lhyperpath existence problem, the Lcyclomatic number problem, the minimum Lcyclomatic set problem, and the minimal Lcyclomatic, Πp, and DP, respectively. set problem are each complete for the complexity class NP, Σ p 2 1
Exploiting Functional Dependence in Query Optimization
, 2000
"... I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions ..."
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Cited by 3 (1 self)
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I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. iii The University of Waterloo requires the signatures of all persons using or photocopying this thesis. Please sign below, and give address and date. Functional dependency analysis can be applied to various problems in query optimization: selectivity estimation, estimation of (intermediate) result sizes, order optimization (in particular sort avoidance), cost estimation, and various problems in the area of semantic query optimization. Dependency analysis in an ansi sql relational model, however, is made complex due to the existence of null values, threevalued logic, outer joins, and duplicate rows. In this thesis we define the notions of strict and lax functional dependencies, strict and lax equivalence constraints, and null constraints, which capture both a