Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

Adaptive sorting algorithms for evaluation of automatic zoning

Optical Character Recognition (OCR) involves analysis of machine-printed and hand written document images. The first step in an OCR process is to locate the text to be recognized on a page. An OCR device tries to identify the characters in these text regions and outputs the characters in ASCII. To evaluate the performance of any OCR device, the ASCII output of the OCR device is compared with the ground truth text which is entered into the computer manually; Some OCR devices provide the users with automatic zoning. The output of any automatic zoning algorithm has to be corrected manually to restore the correct reading order. This is done by elementary edit operations such as insertions, deletions and substitutions or by moving sub-strings of characters. The efficiency of an automatic zoning algorithm is measured by the cost of correcting the OCR generated text. The model for cost calculation requires movement of sub-strings in a particular fashion to ensure minimal cost. This problem has been modeled as sorting an arbitrary permutation. This thesis presents few adaptive sorting approaches which can be incorporated into the automatic zoning evaluation algorithm. These algorithms perform better than the existing algorithms used for this purpose. This thesis also presents more directions in which the problem can be pursued to achieve better performance

09171 Abstracts Collection -- Adaptive, Output Sensitive, Online and Parameterized Algorithms

From 19.01. to 24.04.2009, the Dagstuhl Seminar 09171 ``Adaptive, Output Sensitive, Online and Parameterized Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Adaptive Algorithms for Weighted Queries on Weighted Binary Relations and Labeled Trees

Keyword queries are extremely easy for a user to write. They have become a standard way to query for information in web search engines and most other information retrieval systems whose users are usually laypersons and might not have knowledge about the database schema or contained data. As keyword queries do not impose any structural constraints on the retrieved information, the quality of the obtained results is far from perfect. However, one can hardly improve it without changing the ways the queries are asked and the methods the information is stored in the database. The purpose of this thesis is to propose a method to improve the quality of the information retrieving by adding weights to the existing ways of keyword queries asking and information storing in the database. We consider weighted queries on two different data structures: weighted binary relations and weighted multi-labeled trees. We propose adaptive algorithms to solve these queries and prove the measures of the complexity of these algorithms in terms of the high-level operations. We describe how these algorithms can be implemented and derive the upper bounds on their complexity in two specific models of computations: the comparison model and the word-RAM model

Smooth heaps and a dual view of self-adjusting data structures

We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within a natural model, to a corresponding BST algorithm with the same cost on a dual sequence of operations (i.e. the same sequence with the roles of time and key-space switched). This is the first general transformation between the two families of data structures. There is a rich theory of dynamic optimality for BSTs (i.e. the theory of competitiveness between BST algorithms). The lack of an analogous theory for heaps has been noted in the literature. Through our connection, we transfer all instance-specific lower bounds known for BSTs to a general model of heaps, initiating a theory of dynamic optimality for heaps. On the algorithmic side, we obtain a new, simple and efficient heap algorithm, which we call the smooth heap. We show the smooth heap to be the heap-counterpart of Greedy, the BST algorithm with the strongest proven and conjectured properties from the literature, widely believed to be instance-optimal. Assuming the optimality of Greedy, the smooth heap is also optimal within our model of heap algorithms. As corollaries of results known for Greedy, we obtain instance-specific upper bounds for the smooth heap, with applications in adaptive sorting. Intriguingly, the smooth heap, although derived from a non-practical BST algorithm, is simple and easy to implement (e.g. it stores no auxiliary data besides the keys and tree pointers). It can be seen as a variation on the popular pairing heap data structure, extending it with a "power-of-two-choices" type of heuristic.Comment: Presented at STOC 2018, light revision, additional figure