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### On the combinatorics of leftist trees

P. Nogueira
2001 Discrete Applied Mathematics
Let 'n be the number of leftist trees with n nodes.  ...  Then the problem of determining average quantities (expected additive weights, in the notation of Kemp (Acta Inform. 26 (1989) 711-740)) related to the distribution of nodes is re-analysed.  ...  To determine (asymptotic) expected additive weights of leftist trees one needs the asymptotic number of leftist trees (with n nodes).  ...

### Page 8495 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews
Fabrizio Luccio (1-PISA-IF; Pisa) 2002k:68035 68P05 68R0S 68W40 Kemp, Rainer (D-FRNK-I; Frankfurt am Main) On the expected number of leftist nodes in simply generated trees. (English summary) J.  ...  average number of leftist nodes appearing in such a tree.  ...

### Folklore confirmed

Larry Carter, Jeanne Ferrante, Clark Thomborson
2003 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '03
However, as has been observed for various node-splitting algorithms, there can be an exponential blowup in the size of the graph. We prove that exponential blowup is unavoidable.  ...  In particular, we show that any reducible graph that is equivalent to the complete graph on n nodes (or to related boundeddegree control flow graphs) must have at least 2 n−1 nodes.  ...  LEFTIST TREES A leftist tree T is simply a rooted binary tree (i.e., each node has either zero or two children), with labels on the leaves. |T | denotes the number of nodes in T .  ...

### Folklore confirmed

Larry Carter, Jeanne Ferrante, Clark Thomborson
2003 SIGPLAN notices
However, as has been observed for various node-splitting algorithms, there can be an exponential blowup in the size of the graph. We prove that exponential blowup is unavoidable.  ...  In particular, we show that any reducible graph that is equivalent to the complete graph on n nodes (or to related boundeddegree control flow graphs) must have at least 2 n−1 nodes.  ...  LEFTIST TREES A leftist tree T is simply a rooted binary tree (i.e., each node has either zero or two children), with labels on the leaves. |T | denotes the number of nodes in T .  ...

### Binomial, Fibonacci, and Pairing Heaps [chapter]

Michael Fredman
2004 Handbook of Data Structures and Applications
The binomial tree B k , for k > 0, is obtained by linking two trees B k−1 together; one tree becomes the leftmost subtree of the other. In general B k has 2 k nodes.  ...  number (each pairing reduces by one the total number of trees present).  ...

### A performance comparison of event calendar algorithms: An empirical approach

Kehsiung Chung, Janche Sang, Vernon Rego
1993 Software, Practice & Experience
In contrast to previous studies based on the standard hold model for evaluation of performance statically, the proposed Markov hold model is more general and can be used to examine how different implementations  ...  To demonstrate the utility of the proposed model, we also include a comparison of the simulation calendar algorithms on a token ring protocol with bursty Markovian packet-traffic.  ...  Acknowledgement The authors gratefully acknowledge the help of Doug Jones in making this research effort possible. Thanks are also due to Jeff Kingston for his help.  ...

### A Tutorial on Specifying Data Structures in Maude

Narciso Martí-Oliet, Miguel Palomino, Alberto Verdejo
2005 Electronical Notes in Theoretical Computer Science
Not only are the simple versions considered but also advanced ones such as AVL and 2-3-4 trees.  ...  The operator attributes available in Maude allow the specification of data based on constructors that satisfy some equational properties, like concatenation of lists which is associative and has the empty  ...  Acknowledgement We warmly thank Ricardo Peña for our discussions on functional implementations of data structures, Manuel Clavel for his work on the ITP and his help in understanding its idiosyncrasies  ...

### A second year course on data structures based on functional programming [chapter]

Manuel Núñez, Pedro Palao, Ricardo Peña
1995 Lecture Notes in Computer Science
In this paper, we make a proposal for a second year course on advanced programming, based on the functional paradigm.  ...  We also claim that, as a consequence of the higher level of abstraction of functional languages, more subjects can be covered in the given amount of time.  ...  Acknowledgments We would like to thank the anonymous referees for the careful reading, and for pointing out some mistakes, of the previous version of this paper.  ...

### A Survey on Priority Queues [chapter]

Gerth Stølting Brodal
2013 Lecture Notes in Computer Science
Since then numerous papers have been published on priority queues. This paper tries to list some of the directions research on priority queues has taken the last 50 years.  ...  Center for Massive Data Algorithms, a Center of the Danish National Research Foundation. 1 We let lg x denote the binary logarithm of x. 2 In the following we denote a data structure storing O(1) words  ...  Acknowledgment The author would like to thank Rolf Fagerberg, Andy Brodnik, Jyrki Katajainen, Amr Elmasry, Jesper Asbjørn Sindahl Nielsen and the anonymous reviewers for valuable input.  ...

### Double-Ended Priority Queues [chapter]

Sartaj Sahni
2004 Handbook of Data Structures and Applications
Let us try this procedure on the interval heap of Figure 8 .13. The query interval is [4, 32].  ...  Acknowledgment This work was supported, in part, by the National Science Foundation under grant CCR-9912395.  ...  For example, if we do a sequence of inserts, every other one simply puts the element in the buffer. The remaining inserts put one element in maxP Q and one in minP Q.  ...

### Modularising inductive families

Hsiang-Shang Ko, Jeremy Gibbons
2011 Proceedings of the seventh ACM SIGPLAN workshop on Generic programming - WGP '11
Different constraints are used in different contexts, leading to different versions of datatypes for the same data structure.  ...  We propose a datatype-generic solution, in which we axiomatise a family of isomorphisms between datatypes and their more refined versions as datatype refinements, and show that McBride's ornaments can  ...  Acknowledgements The first author is supported by the University of Oxford Clarendon Fund Scholarship, and both authors by the UK Engineering and Physical Sciences Research Council project Reusability  ...

### Modularising inductive families

Hsiang-Shang KO, Jeremy GIBBONS
2013 Progress in Informatics
Different constraints are used in different contexts, leading to different versions of datatypes for the same data structure.  ...  We propose a datatype-generic solution, in which we axiomatise a family of isomorphisms between datatypes and their more refined versions as datatype refinements, and show that McBride's ornaments can  ...  Acknowledgements The first author is supported by the University of Oxford Clarendon Fund Scholarship, and both authors by the UK Engineering and Physical Sciences Research Council project Reusability  ...

### Document Listing on Repetitive Collections with Guaranteed Performance [article]

Gonzalo Navarro
2018 arXiv   pre-print
We show that the idea has independent interest: we introduce the first grammar-based index that, on a text T[1,N] with a grammar of size r, uses O(r N) bits and counts the number of occurrences of a pattern  ...  In particular, we focus on repetitive collections: a collection of size N over alphabet [1,σ] is composed of D copies of a string of size n, and s edits are applied on ranges of copies.  ...  All the internal nodes of this tree are distinct nonterminal symbols (unless they generate the same strings), and end up in a root symbol S 1 . Now we regard the subsequent documents one by one.  ...

### FunSeqSet: Towards a Purely Functional Data Structure for the Linearisation Case of Dynamic Trees Problem [article]

Juan Carlos Saenz-Carrasco
2019 arXiv   pre-print
(i.e. sets) data structures in order to manage efficiently k-ary trees for the linearisation case of the dynamic trees problem.  ...  We present FunSeqSet, based on the primitive version of finger trees, i.e. the de facto sequence data structure for the purely functional programming language Haskell, augmented with variants of the collection  ...  Supported by Consejo Nacional de Ciencia y Tecnologa -CONACYT (the Mexican National Council for Science and Technology) for the financial support under the grant no. 580617/411550 and registration no.  ...

### Bootstrapping one-sided flexible arrays

Ralf Hinze
2002 SIGPLAN notices
In particular, one can trade the running time of look-up operations for the running time of update operations.  ...  We show that different tree shapes can be conveniently modelled after mixedradix number systems.  ...  Acknowledgements I am indebted to Chris Okasaki for a very stimulating discussion on functional arrays (the idea of trading the running time of lookup operations for the running time of update operations  ...
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