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- Arash Farzan, J. Ian Munro
- Algorithmica
- 2012

We propose a uniform method to encode various types of trees succinctly. These families include ordered (ordinal), k-ary (cardinal), and unordered (free) trees. We will show the approach is intrinsically suitable for obtaining entropy-based encodings of trees (such as the degree-distribution entropy). Previously-existing succinct encodings of trees use ad… (More)

- Arash Farzan, J. Ian Munro
- ESA
- 2008

We consider the problem of encoding a graph with n ver-tices and m edges compactly supporting adjacency, neighborhood and degree queries in constant time in the log n-bit word RAM model. The adjacency query asks whether there is an edge between two vertices, the neighborhood query reports the neighbors of a given vertex in constant time per neighbor, and… (More)

- Arash Farzan, J. Ian Munro
- SWAT
- 2008

We propose a uniform approach for succinct representation of various families of trees. The method is based on two recursive decomposition of trees into subtrees. Recursive decomposition of a structure into substructures is a common technique in succinct data structures and has been shown fruitful in succinct representation of ordinal trees [7, 10] and… (More)

- Peyman Afshani, Ehsan Chiniforooshan, +4 authors Hamid Zarrabi-Zadeh
- COCOON
- 2007

We investigate the problem of finding an unknown cut through querying vertices of a graph G. Our complexity measure is the number of submitted queries. To avoid some worst cases, we make a few assumptions which allow us to obtain an algorithm with the worst case query complexity of O(k) + 2k log n k in which k is the number of vertices adjacent to… (More)

- Guy E. Blelloch, Arash Farzan
- CPM
- 2010

We consider the problem of highly space-efficient representation of separable graphs while supporting queries in constant time in the RAM with logarithmic word size. In particular, we show constant-time support for adjacency, degree and neighborhood queries. For any monotone class of separable graphs, the storage requirement of the representation is optimal… (More)

- Arash Farzan, Rajeev Raman, S. Srinivasa Rao
- ICALP
- 2009

We consider the succinct representation of ordinal and cardinal trees on the RAM with logarithmic word size. Given a tree T , our representations support the following operations in O(1) time: (i) BP-substring(i, b), which reports the substring of length b bits (b is at most the wordsize) beginning at position i of the balanced parenthesis representation of… (More)

- Arash Farzan, J. Ian Munro
- Theor. Comput. Sci.
- 2011

- Mahtab Nouri, Amir Hossein Abdi, Arash Farzan, Faraneh Mokhtarpour, AliReza Akbarzadeh Baghban
- American journal of orthodontics and dentofacial…
- 2014

INTRODUCTION
In this study, we aimed to measure the inclination of teeth on dental casts by a manual technique with the tooth inclination protractor (TIP; MBI, Newport, United Kingdom) and a newly designed 3-dimensional (3D) software program. The correlation of the 2 techniques was evaluated, and the reliability of each technique was assessed separately.
… (More)

- Arash Farzan, Travis Gagie, Gonzalo Navarro
- Comput. Geom.
- 2010

We give the first fully compressed representation of a set of m points on an n×n grid, taking H +o(H) bits of space, where H = lg n 2 m is the entropy of the set. This representation supports range counting, range reporting, and point selection queries, with a performance that is comparable to that of uncompressed structures and that improves upon the only… (More)

- Arash Farzan, Shahin Kamali
- Algorithmica
- 2011

Given an unlabeled, unweighted, and undirected graph with n vertices and small (but not necessarily constant) treewidth k, we consider the problem of preprocessing the graph to build space-efficient encodings (oracles) to perform various queries efficiently. We assume the word RAM model where the size of a word is Ω(logn) bits. The first oracle, we present,… (More)