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The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 634 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
A primal method for minimal cost flows, with applications to the assignment and transportation problems
, 1967
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Vertex Heaviest Paths and Cycles in QuasiTransitive Digraphs
 Discrete Math
"... A digraph D is called a quasitransitive digraph (QTD) if for any triple x; y; z of distinct vertices of D such that (x; y) and (y; z) are arcs of D there is at least one arc from x to z or from z to x. Solving a conjecture by J. BangJensen and J. Huang (J. Graph Theory, to appear), G. Gutin (Austr ..."
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Cited by 10 (9 self)
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A digraph D is called a quasitransitive digraph (QTD) if for any triple x; y; z of distinct vertices of D such that (x; y) and (y; z) are arcs of D there is at least one arc from x to z or from z to x. Solving a conjecture by J. BangJensen and J. Huang (J. Graph Theory, to appear), G. Gutin (Australas. J. Combin., to appear) described polynomial algorithms for finding a Hamiltonian cycle and a Hamiltonian path (if it exists) in a QTD. The approach taken in that paper cannot be used to find a longest path or cycle in polynomial time. We present a principally new approach that leads to polynomial algorithms for finding vertex heaviest paths and cycles in QTD's with nonnegative weights on the vertices. This, in particular, provides an answer to a question by N. Alon on longest paths and cycles in QTD's. 1 Introduction A digraph D is called quasitransitive if for any triple x; y; z of distinct vertices of D such that (x; y) and (y; z) are arcs of D there is at least one arc from x to ...
On an Algorithm of Zemlyachenko for Subtree Isomorphism
 Inform. Process. Lett
, 1998
"... Zemlyachenko's linear time algorithm for free tree isomorphism is unique in that it also partitions the set of rooted subtrees of a given rooted tree into isomorphism equivalence classes. Unfortunately, his algorithm is very hard to follow. In this note, we use modern data structures to explain ..."
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Cited by 4 (0 self)
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Zemlyachenko's linear time algorithm for free tree isomorphism is unique in that it also partitions the set of rooted subtrees of a given rooted tree into isomorphism equivalence classes. Unfortunately, his algorithm is very hard to follow. In this note, we use modern data structures to explain and implement Zemlyachenko's scheme. We give a full description of a free rendition of his method using some of his ideas and adding some new ones; in particular, the data structures are new. email: fdititz, itai, rodehg@cs.technion.ac.il 1 1 Introduction Free tree isomorphism is a well known problem which has many applications. A linear time algorithm to solve the problem has been developed by Hopcroft and Tarjan [2], who used it to devise a linear planarity test. Several other linear algorithms were suggested [1, pp.196199], [3], [4]. The common approach is as follows. First, free tree isomorphism is reduced to the rooted case. The root is set canonically at the central vertex or at the ...
Earliest Arrival Contraflow Problem on SeriesParallel Graphs
, 2013
"... Abstract ⎯ Both the earliest arrival flow and the contraflow problems have been highly focused in the research of evacuation planning. We formulated the earliest arrival contraflow problem, where as many evacuees as possible should be sent from dangerous places to safe destinations in every time per ..."
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Abstract ⎯ Both the earliest arrival flow and the contraflow problems have been highly focused in the research of evacuation planning. We formulated the earliest arrival contraflow problem, where as many evacuees as possible should be sent from dangerous places to safe destinations in every time period by reversing the direction of roads at time zero. A strongly polynomial time algorithm for the earliest arrival contraflow problem on a twoterminal seriesparallel graph model having capacities and transit times on the arcs has been presented.
Masters by Research in The Design and Evaluation of Advanced Interactive Systems
, 2002
"... An exploratory experimental study was conducted investigating the use and development of World Wide Web History Mechanisms. The study employed two stages of investigation. A combination of screen evaluations and interviews were used with six participants to create a research agenda of key usability ..."
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An exploratory experimental study was conducted investigating the use and development of World Wide Web History Mechanisms. The study employed two stages of investigation. A combination of screen evaluations and interviews were used with six participants to create a research agenda of key usability issues within the history domain. The participants revealed a strong preference for sorting (organising) information whilst browsing, personalising pages more, and text based hierarchical systems. It was decided that further examination of sorting strategies would yield the greatest potential for augmenting history mechanism design. In consequence, the second stage required a more quantitative means to compare the sorting strategies. Ten participants performed a repeated web sorting and retrieval task with Microsoft Internet Explorer “Favourites ” over two days. The results contradicted the user’s preferences in the first study where sorting the web information after browsing induced significantly better retrieval times, accuracy, and subjective satisfaction. Surprisingly, sorting information after browsing took
Connected (g,f)Factors and Supereulerian Digraphs
"... Given a digraph (an undirected graph, resp.) D and two positive integers f(x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)factor if g(x) d + H (x) = d \Gamma H (x) f(x)(g(x) dH (x) f(x), resp.) for every x 2 V (D). If f(x) = g(x) = 1 for every x, then a connected (g; f) ..."
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Given a digraph (an undirected graph, resp.) D and two positive integers f(x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)factor if g(x) d + H (x) = d \Gamma H (x) f(x)(g(x) dH (x) f(x), resp.) for every x 2 V (D). If f(x) = g(x) = 1 for every x, then a connected (g; f)factor is a hamiltonian cycle. The previous research related to the topic has been carried out either for (g; f)factors (in general, disconnected) or for hamiltonian cycles separately, even though numerous similarities between them have been recently detected. Here we consider connected (g; f)factors in digraphs and show that several results on hamiltonian digraphs, which are generalizations of tournaments, can be extended to connected (g; f)factors. Applications of these results to supereulerian digraphs are also obtained. 1 Introduction and terminology Given a digraph (an undirected graph, resp.) D and two positive integers f(x); g(x) for every x 2 V (D), a subgraph H of D is called ...