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UMLDiff: An Algorithm for ObjectOriented Design Differencing
, 2005
"... This paper presents UMLDiff, an algorithm for automatically detecting structural changes between the designs of subsequent versions of objectoriented software. It takes as input two class models of a Java software system, reverse engineered from two corresponding code versions. It produces as outpu ..."
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Cited by 72 (5 self)
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This paper presents UMLDiff, an algorithm for automatically detecting structural changes between the designs of subsequent versions of objectoriented software. It takes as input two class models of a Java software system, reverse engineered from two corresponding code versions. It produces as output a change tree, i.e., a tree of structural changes, that reports the differences between the two design versions in terms of (a) additions, removals, moves, renamings of packages, classes, interfaces, fields and methods, (b) changes to their attributes, and (c) changes of the dependencies among these entities. UMLDiff produces an accurate report of the design evolution of the software system, and enables subsequent designevolution analyses from multiple perspectives in support of various evolution activities. UMLDiff and the analyses it enables can assist software engineers in their tasks of understanding the rationale of design evolution of the software system and planning future development and maintenance activities. We evaluate UMLDiff’s correctness and robustness through a realworld case study.
An Efficient Graph Algorithm for Dominance Constraints
 JOURNAL OF ALGORITHMS
, 2003
"... Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NPcomplete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in dete ..."
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Cited by 37 (15 self)
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Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NPcomplete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiablity in deterministic polynomial time. Previously, no polynomial time algorithm was known.
Efficiently Answering Reachability Queries on Very Large Directed Graphs
"... Efficiently processing queries against very large graphs is an important research topic largely driven by emerging real world applications, as diverse as XML databases, GIS, web mining, social network analysis, ontologies, and bioinformatics. In particular, graph reachability has attracted a lot of ..."
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Cited by 22 (3 self)
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Efficiently processing queries against very large graphs is an important research topic largely driven by emerging real world applications, as diverse as XML databases, GIS, web mining, social network analysis, ontologies, and bioinformatics. In particular, graph reachability has attracted a lot of research attention as reachability queries are not only common on graph databases, but they also serve as fundamental operations for many other graph queries. The main idea behind answering reachability queries in graphs is to build indices based on reachability labels. Essentially, each vertex in the graph is assigned with certain labels such that the reachability between any two vertices can be determined by their labels. Several approaches have been proposed for building these reachability labels; among them are interval labeling (tree cover) and 2hop labeling. However, due to the large number of vertices in many real world graphs (some graphs can easily contain millions of vertices), the computational cost and (index) size of the labels using existing methods would prove too expensive to be practical. In this paper, we introduce a novel graph structure, referred to as pathtree, to help labeling very large graphs. The pathtree cover is a spanning subgraph of G in a tree shape. We demonstrate both analytically and empirically the effectiveness of our new approaches.
Algorithms for dense graphs and networks on the random access computer, Algorithmica 15
, 1996
"... Abstract. We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size L = f2 (log n) a maximal matching in an nvertex bipartite graph in time O (n 2 + n2"5/~.) = O (n2"5/log n), how to comp ..."
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Cited by 18 (5 self)
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Abstract. We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size L = f2 (log n) a maximal matching in an nvertex bipartite graph in time O (n 2 + n2"5/~.) = O (n2"5/log n), how to compute the transitive closure of a digraph with n vertices and m edges in time O(n 2 + nm/,k), how to solve the uncapacitated transportation problem with integer costs in the range [0..C] and integer demands in the range [U..U] in time O ((n 3 (log log / log n) 1/2 + n 2 log U) log nC), and how to solve the assignment problem with integer costs in the range [0..C] in time O(n 2"5 lognC/(logn/loglogn)l/4). Assuming a suitably compressed input, we also show how to do depthfirst and breadthfirst search and how to compute strongly connected components and biconnected components in time O(n~. + n2/L), and how to solve the single source shortestpath problem with integer costs in the range [0..C] in time O (n 2 (log C)/log n). For the transitive closure algorithm we also report on the experiences with an implementation. Key Words.
Markov Processes Involving qStirling Numbers
 Combinatorics, Probability and Computing
, 1997
"... In this paper we consider the Markov process defined by P 1;1 = 1; P n;` = (1 \Gamma n;` ) \Delta P n\Gamma1;` + n;`\Gamma1 \Delta P n\Gamma1;`\Gamma1 for transition probabilities n;` = q ` and n;` = q n\Gamma1 . We give closed forms for the distributions and the moments of the underlying ra ..."
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Cited by 4 (2 self)
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In this paper we consider the Markov process defined by P 1;1 = 1; P n;` = (1 \Gamma n;` ) \Delta P n\Gamma1;` + n;`\Gamma1 \Delta P n\Gamma1;`\Gamma1 for transition probabilities n;` = q ` and n;` = q n\Gamma1 . We give closed forms for the distributions and the moments of the underlying random variables. Thereby we observe that the distributions can be easily described in terms of qStirling numbers of the second kind. Their occurrence in a purely time dependent Markov process allows a natural approximation for these numbers through the normal distribution. We also show that these Markov processes describe some parameters related to the study of random graphs as well as to the analysis of algorithms. Keywords: qStirling numbers, Markov processes, random graphs, approximate counting. 1 Introduction In this paper we will study the Markov process defined by P 1;1 = 1 P n;` = 0 for ` = 2 f 1; : : : ; n g and (1) P n;` = (1 \Gamma n;` ) P n\Gamma1;` + n;`\Gamma1 P n\Gamma1;...
On the Distribution of the Transitive Closure in a Random Acyclic Digraph
 Microsoft, One Microsoft Way, Redmond, Washington 980526399 Department of Mathematics, The Ohio state University
, 1993
"... . In the usual Gn;pmodel of a random acyclic digraph let fl n (1) be the size of the reflexive, transitive closure of node 1, a source node; then the distribution of fl n (1) is given by 8 1 h n : Pr ( fl n (1) = h ) = q n\Gammah h\Gamma1 Y i=1 (1 \Gamma q n\Gammai ) ; where q = ..."
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Cited by 4 (1 self)
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. In the usual Gn;pmodel of a random acyclic digraph let fl n (1) be the size of the reflexive, transitive closure of node 1, a source node; then the distribution of fl n (1) is given by 8 1 h n : Pr ( fl n (1) = h ) = q n\Gammah h\Gamma1 Y i=1 (1 \Gamma q n\Gammai ) ; where q = 1 \Gamma p. Our analysis points out some surprising relations between this distribution and known functions of the number theory. In particular we find for the expectation of fl n (1): lim n!1 n \Gamma E(fl n (1)) = L(q) where L(q) = P 1 i=1 q i =(1 \Gamma q i ) is the socalled Lambert Series, which corresponds to the generating function of the divisorfunction. These results allow us to improve the expected running time for the computation of the transitive closure in a random acyclic digraph and in particular we can ameliorate in some cases the analysis of the Goralc'ikov'aKoubek Algorithm. 1 Introduction Let G = (V; E) be a directed graph, defined by a vertex set V = ...
Kreach: Who is in your small world
 PVLDB
"... We study the problem of answering khop reachability queries in a directed graph, i.e., whether there exists a directed path of length k, from a source query vertex to a target query vertex in the input graph. The problem of khop reachability is a general problem of the classic reachability (where ..."
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Cited by 3 (2 self)
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We study the problem of answering khop reachability queries in a directed graph, i.e., whether there exists a directed path of length k, from a source query vertex to a target query vertex in the input graph. The problem of khop reachability is a general problem of the classic reachability (where k = ∞). Existing indexes for processing classic reachability queries, as well as for processing shortest path queries, are not applicable or not efficient for processing khop reachability queries. We propose an index for processing khop reachability queries, which is simple in design and efficient to construct. Our experimental results on a wide range of real datasets show that our index is more efficient than the stateoftheart indexes even for processing classic reachability queries, for which these indexes are primarily designed. We also show that our index is efficient in answering khop reachability queries. 1.
qDistributions in Random Graphs: Transitive Closure and Reduction
, 1995
"... One of the classical topics in discrete mathematics and in computer science is the computation of the transitive closure and reduction of a directed graph. We provide a complete analysis of the random variables counting the size of the transitive closure and reduction in random acyclic digraphs. In ..."
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Cited by 2 (2 self)
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One of the classical topics in discrete mathematics and in computer science is the computation of the transitive closure and reduction of a directed graph. We provide a complete analysis of the random variables counting the size of the transitive closure and reduction in random acyclic digraphs. In particular we present closed forms for their probability distribution and moments, showing that they involve functions such as the qbinomial coefficients and the qStirling numbers of the second kind. In general it turns out that a pure numbertheoretical notation, the qnotation, represents the perfect tool to deal with these kinds of problems. In this context we speak therefore about qdistributions. 1 Introduction Graphs are probably the most common "abstract" structure in computer science and because of their flexibility they provide an adequate model for a variety of problems. Any system consisting of a set V of discrete states (called nodes or vertices) and a set E of relations b...
qDistributions and Markov Processes
, 1996
"... We consider a sequence of integervalued random variables Xn ; n 1; representing a special Markov process with transition probability n;` , satisfying P n;` = (1\Gamma n;` ) Pn\Gamma1;` + n;`\Gamma1 Pn\Gamma1;`\Gamma1 : Whenever the transition probability is given by n;` = q ff n+fi `+fl and ..."
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Cited by 2 (0 self)
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We consider a sequence of integervalued random variables Xn ; n 1; representing a special Markov process with transition probability n;` , satisfying P n;` = (1\Gamma n;` ) Pn\Gamma1;` + n;`\Gamma1 Pn\Gamma1;`\Gamma1 : Whenever the transition probability is given by n;` = q ff n+fi `+fl and n;` = 1 \Gamma q ff n+fi `+fl , we can find closed forms for the distribution and the moments of the corresponding random variables, showing that they involve functions such as the qbinomial coefficients and the qStirling numbers. In general it turns out that the qnotation, up to now mainly used in the theory of qhypergeometrical series, represents a powerful tool to deal with these kinds of problems. In this context we speak therefore about qdistributions. Finally, we present some possible, mainly graph theoretical interpretations of these random variables for special choices of ff; fi and fl. 1 Introduction The most common complexity measure in the running time analysis of alg...