Eduardo Fernandes Barbosa

Hierarchies of indices for text searching

The objective of this paper is to present an efficient implementation of a recently known index for text databases presented in the literature, when the database is stored on secondary storage devices such as magnetic or optical disks. The implementation is built on top of a new and simple index for texts called pat array (also called suffix array). Considering that text searching in a large database spends most of the time accessing external storage devices, we propose additional indices structures and searching algorithms for pat arrays that reduce the number of disk accesses. We present two index structures: a two-level hierarchy model that uses the main memory and one level of external storage (magnetic or optical devices) and a three-level hierarchy model that uses the main memory and two levels of external storage (magnetic and optical devices). Performance improvement is achieved in both models by storing most of higher index levels in faster memories, thus reducing accesses in the slowest devices in the hierarchy. Analytical results and performance gains are presented for both models. Further improvements for text searching with these models (such as index compression) are also proposed.

Binary Searching with Nonuniform Costs and Its Application to Text Retrieval

Abstract. We study the problem of minimizing the expected cost of binary searching for data where the access cost is not fixed and depends on the last accessed element, such as data stored in magnetic or optical disk. We present an optimal algorithm for this problem that finds the optimal search strategy in O(n3) time, which is the same time complexity of the simpler classical problem of fixed costs. Next, we present two practical linear expected time algorithms, under the assumption that the access cost of an element is independent of its physical position. Both practical algorithms are online, that is, they find the next element to access as the search proceeds. The first one is an approximate algorithm which minimizes the access cost disregarding the goodness of the problem partitioning. The second one is a heuristic algorithm, whose quality depends on its ability to estimate the final search cost, and therefore it can be tuned by recording statistics of previous runs. We present an application for our algorithms related to text retrieval. When a text collection is large it demands specialized indexing techniques for efficient access. One important type of index is the suffix array, where data access is provided through an indirect binary search on the text stored in magnetic disk or optical disk. Under this cost model we prove that the optimal algorithm cannot perform better than Ω(1/ log n) times the standard binary search. We also prove that the approximate strategy cannot, on average, perform worse than 39% over the optimal one. We confirm the analytical results with simulations, showing improvements between 34% (optimal) and 60% (online) over standard binary search for both magnetic and optical disks.

Optimized Binary Search and Text Retrieval

We present an algorithm that minimizes the expected cost of indirect binary search for data with non-constant access costs, such as disk data. Indirect binary search means that sorted access to the data is obtained through an array of pointers to the raw data. One immediate application of this algorithm is to improve the retrieval performance of disk databases that are indexed using the suffix array model (also called PAT array). We consider the cost model of magnetic and optical disks and the anticipated knowledge of the expected size of the subproblem produced by reading each disk track. This information is used to devise a modified binary searching algorithm to decrease overall retrieval costs. Both an optimal and a practical algorithm are presented, together with analytical and experimental results. For 100 megabytes of text the practical algorithm costs 60% of the standard binary search cost for the magnetic disk and 65% for the optical disk.

Data structures and access methods for read-only optical disks

This paper presents alternatives for efficient file organization and placement on read-only optical disks, known as CD-ROM. We extend an analytical model for retrieval costs found in the literature, adding additional aspects to the model, such as rotational latency and file structure. From CD-ROM standards we derive algorithms for file mapping and access time calculations to build a deterministic model which is used in simulations. Experimental results on different file structures and file sizes show that rotational latency, file size, file structure, and file allocation strongly affects the retrieval performance in CD-ROM disks. A comparative study considering a sequence of accesses to sequential, indexed sequential, B-tree and hashing file structures shows that hashing and indexed sequential are the organizations that presented the smallest total time under the limitations of optical devices. We present an indexed sequential organization for CD-ROM file systems which minimizes disk accesses.