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An Incremental Algorithm for a Generalization of the ShortestPath Problem
, 1992
"... The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsume ..."
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Cited by 121 (1 self)
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The grammar problem, a generalization of the singlesource shortestpath problem introduced by Knuth, is to compute the minimumcost derivation of a terminal string from each nonterminal of a given contextfree grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the singlesource shortestpath problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortestpath problem is its ability to handle "multiple heterogeneous modifications": between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edgelength changes.
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 106 (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 26 (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...
Directed Hypergraphs as a Modelling Paradigm
 RIVISTA AMASES
, 1999
"... We address a generalization of graphs, the directed hypergraphs, and show that they are a powerful tool in modelling and solving several relevant problems in many application areas. Such application areas include Linear Production Problems, Flexible Manufacturing Systems, Propositional Logic, Relat ..."
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Cited by 12 (1 self)
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We address a generalization of graphs, the directed hypergraphs, and show that they are a powerful tool in modelling and solving several relevant problems in many application areas. Such application areas include Linear Production Problems, Flexible Manufacturing Systems, Propositional Logic, Relational Databases, and Public Transportation Systems.
Hypergraph Models And Algorithms For The Assembly Problem
, 1992
"... We consider the problem of finding an optimal set of feasible assembly operations in order to derive a desired product from a given set of parts. We show that optimal solutions, under different objective functions, can be obtained by means of computationally efficient hypergraph algorithms. In parti ..."
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Cited by 7 (1 self)
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We consider the problem of finding an optimal set of feasible assembly operations in order to derive a desired product from a given set of parts. We show that optimal solutions, under different objective functions, can be obtained by means of computationally efficient hypergraph algorithms. In particular, we consider the case in which one wants to minimize the duration with an unlimited degree of parallelism. Finally, a new fast algorithm is presented in order to assign operations to robots in an optimal way when the degree of parallelism is bounded. Technical Report TR6/92 March, 1992 (revised: July, 1992) This research has been supported by "Ministero dell'Universit e della Ricerca Scientifica e Tecnologica", National Project on "Gestione dei flussi nei sistemi flessibili di produzione". 2 Introduction In robotic assembly systems, one or more types of items are produced by assembling together several parts given in input, according to a properly defined assembly plan. An asse...
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...
The Satisfiability problem for the SchöenfinkelBernays fragment: Partial Instantiation and Hypergraph Algorithms
 Proceedings of 8th subcommission &quot;Magnetic
, 1994
"... A partial instantiation approach to the solution of the satisfiability problem in the SchoenfinkelBernays fragment of 1 st order logic is presented. It is based on a reduction of the problem to a finite sequence of satisfiability problems in the propositional logic and it improves upon the ori ..."
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Cited by 4 (2 self)
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A partial instantiation approach to the solution of the satisfiability problem in the SchoenfinkelBernays fragment of 1 st order logic is presented. It is based on a reduction of the problem to a finite sequence of satisfiability problems in the propositional logic and it improves upon the original idea of partial instantiation, as proposed by Jeroslow. In the second part of the paper a new interpretation of the partial instantiation approach in terms of Directed Hypergraphs is proposed and a particular implementation for the Datalog case is described in detail. 1 Introduction. The problem of Logical Inference plays a fundamental role in Decision Sciences and has several applications in fields such as decision support systems, logic circuit design, data bases, and programming languages. Although classical approaches to formalize and solve inference problems have been of symbolic nature, in the last few years many scientists in the Operations Research community have studied ...
From Program Synthesis to Optimal Program Synthesis
"... Abstract—In many practical situations, we know the values of some quantities x1,..., xn, we know the relations between these quantities, the desired quantity y, and maybe some auxiliary quantities, and we want to estimate y. There exist automatic tools for such estimations – called program synthesis ..."
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Abstract—In many practical situations, we know the values of some quantities x1,..., xn, we know the relations between these quantities, the desired quantity y, and maybe some auxiliary quantities, and we want to estimate y. There exist automatic tools for such estimations – called program synthesis tools. A program synthesis tool usually generates a program for computing y. In many cases, however, several such programs are possible, and it is desirable to generate the optimal (e.g., the fastest) program. In this paper, we describe algorithms aimed at such optimal program synthesis. The problem can be interpreted in logical terms, as assigning fuzzystyle degrees to rules describing relations between variables. I. NEED FOR DATA PROCESSING: A BRIEF REMINDER One of the main objectives of science: an informal description. One of the main objectives of science is to describe the
Hypergraphs and fast mining of association rules
, 2003
"... This report presents the work of the first year of my Ph.D, and the main fields of my research activity. The activities I’ve done in this past year can be summarized as follows: Nov. 2002Jun. 2003: I started my doctorate working in the field of Information Retrieval Jul. 2003: I followed a two week ..."
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This report presents the work of the first year of my Ph.D, and the main fields of my research activity. The activities I’ve done in this past year can be summarized as follows: Nov. 2002Jun. 2003: I started my doctorate working in the field of Information Retrieval Jul. 2003: I followed a two weeks summer school at Lipari focused on “Data Mining and Pattern Matching” May. 2003now: I started to study directed hypergraph, and in particular I focused on algorithms for optimal hyperpaths. I’ll consider their use on making inference on sets of association rules. In the next sections I’ll explain my research field and what are my plans for the future research. In Section 1, I introduce the field of association rules mining and describe the stateoftheart techniques for rules mining. In Section 2, I introduce directed hypergraphs and algorithms for finding optimal hyperpaths. In Section 3, I show the use of directed hypergraphs to model association rules with hypergraph and to do inference with them.
Empirical analysis and optimization of an NPhard algorithm using CSP and FDR
"... Abstract. In many cases where an algorithm is provably NPhard, this intractability is a worstcase bound that only applies to pathological inputs. In these cases, by exploiting knowledge of the specific structure of “realworld ” inputs, the algorithm can be shown to be much more efficient in the “ ..."
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Abstract. In many cases where an algorithm is provably NPhard, this intractability is a worstcase bound that only applies to pathological inputs. In these cases, by exploiting knowledge of the specific structure of “realworld ” inputs, the algorithm can be shown to be much more efficient in the “normal ” case. However, when studying a new problem, this can be hard to show if it is not obvious which structural constraints exist, and which ones would lead to increases in efficiency. In this paper, we show how one can describe the underlying problem declaratively as a CSP process and use the FDR refinement checker to explore the complexity space of the problem. By knowing which optimizations FDR uses to find solutions more efficiently, we can determine under which conditions the worstcase intractable algorithm executes efficiently, and incorporate analogous optimizations into the algorithm to exploit these conditions. 1.