. Initially introduced in the late 1960s and early 1970s, dynamic programming algorithms have become increasingly popular in automatic speech recognition. There are two reasons why this has occurred: First, the dynamic programming strategy can be combined with avery e#cient and practical pruning strategy so that very large search spaces can be handled. Second, the dynamic programming strategy has turned out to be extremely #exible in adapting to new requirements. Examples of such requirements are the lexical tree organization of the pronunciation lexicon and the generation of a word graph instead of the single best sentence. In this paper, we attempt to systematically review the use of dynamic programming search strategies for small#vocabulary and large#vocabulary continuous speech recognition. The following methods are described in detail: search using a linear lexicon, search using a lexical tree, language-model look-ahead and word graph generation. 1 Introduction Search strategie...

We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k+n log n) and O(n) working space. The algorithm uses only one advanced data structure, namely a splittable queue. We introduce (weakly) greedy pseudo--triangulations, whose combinatorial properties are crucial for our method. 1 Introduction Consider a collection O of pairwise disjoint convex objects in the plane. We are interested in problems in which these objects arise as obstacles, either in connection with visibility problems where they can block the view from an other geometric object, or in motion planning, where these objects may prevent a moving object from moving along a straight line path. The visibility graph is a central object in such contexts. For polygonal obstacles the vertices of these polygons are the nodes of the visibility graph, and two nodes are connected by an arc if the corresponding vertices can see each other. [9] describes the first non-triv...

We present new improved algorithms for the sorting problem. The algorithms are not only efficient but also clear and simple. First, we introduce Forward Radix Sort which combines the advantages of traditional left-to-right and right-to-left radix sort in a simple manner. We argue that this algorithm will work very well in practice. Adding a preprocessing step, we obtain an algorithm with attractive theoretical properties. For example, n binary strings can be sorted in \Theta i n log i B n log n + 2 jj time, where B is the minimum number of bits that have to be inspected to distinguish the strings. This is an improvement over the previously best known result by Paige and Tarjan. The complexity may also be expressed in terms of H, the entropy of the input: n strings from a stationary ergodic process can be sorted in \Theta \Gamma n log \Gamma 1 H + 1 \Delta\Delta time, an improvement over the result recently presented by Chen and Reif.

We present a fairly general method for finding deterministic constructions obeying what we call k- restrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n; k)-universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2 configurations appear) and families of perfect hash functions. The near-optimal constructions of these objects imply the very efficient derandomization of algorithms in learning, of fixed-subgraph finding algorithms, and of near optimal \Sigma\Pi\Sigma threshold formulae. In addition, they derandomize the reduction showing the hardness of approximation of set cover. They also yield deterministic constructions for a local-coloring protocol, and for exhaustive testing of circuits.

A program checker verifies that a particular program execution is correct. We give simple and efficient program checkers for some basic geometric tasks. We report about our experiences with program checking in the context of the LEDA system. We discuss program checking for data structures that have to rely on user-provided functions.

Abstract. We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map dX/ [ with n vertices and apply it to the development of a unified dynamic data structure that supports pointlocation, ray-shooting, and shortest-path queries in A4. The space requirement is O(n log n). Point-location queries take time O(log n). Ray-shooting and shortest-path queries take time O(log n) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take O(log n) time (amortized for vertex updates). This is the first polylog-time dynamic data structure for shortest-path and ray-shooting queries. It is also the first dynamic point-location data structure for connected planar maps that achieves optimal query time. Key words, point location, ray shooting, shortest path, computational geometry, dynamic algorithm

B-trees are the data structure of choice for maintaining searchable data on disk. However, B-trees perform suboptimally • when keys are long or of variable length, • when keys are compressed, even when using front compression, the standard B-tree compression scheme, • for range queries, and • with respect to memory effects such as disk prefetching. This paper presents a cache-oblivious string B-tree (COSB-tree) data structure that is efficient in all these ways: • The COSB-tree searches asymptotically optimally and inserts and deletes nearly optimally. • It maintains an index whose size is proportional to the frontcompressed size of the dictionary. Furthermore, unlike standard front-compressed strings, keys can be decompressed in a memory-efficient manner. • It performs range queries with no extra disk seeks; in contrast, B-trees incur disk seeks when skipping from leaf block to leaf block. • It utilizes all levels of a memory hierarchy efficiently and makes good use of disk locality by using cache-oblivious layout strategies.

We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o( # n) per operation. To be precise, the algorithm uses O(n 1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and, bipartiteness in amortized time O(n 1/3 log n) per update, with O(1) worst case time per query.

A family of functions F that map [0; n] 7! [0; n], is said to be h-wise independent if any h points in [0; n] have an image, for randomly selected f 2 F , that is uniformly distributed. This paper gives both probabilistic and explicit randomized constructions of n ffl -wise independent functions, ffl ! 1, that can be evaluated in constant time for the standard random access model of computation. Simple extensions give comparable behavior for larger domains. As a consequence, many probabilistic algorithms can for the first time be shown to achieve their expected asymptotic performance for a feasible model of computation. This paper also establishes a tight tradeoff in the number of random seeds that must be precomputed for a random function that runs in time T and is h-wise independent. Categories and Subject Descriptors: E.2 [Data Storage Representation]: Hash-table representation; F.1.2 [Modes of Computation]: Probabilistic Computation; F2.3 [Tradepffs among Computational Measures]...

Abstract. We present cache-oblivious data structures based upon exponential structures. These data structures perform well on a hierarchical memory but do not depend on any parameters of the hierarchy, including the block sizes and number of blocks at each level. The problems we consider are searching, partial persistence and planar point location. On a hierarchical memory where data is transferred in blocks of size B, some of the results we achieve are: – We give a linear-space data structure for dynamic searching that supports searches and updates in optimal O(log B N) worst-case I/Os, eliminating amortization from the result of Bender, Demaine, and Farach-Colton (FOCS ’00). We also consider finger searches and updates and batched searches. – We support partially-persistent operations on an ordered set, namely, we allow searches in any previous version of the set and updates to the latest version of the set (an update creates a new version of the set). All operations take an optimal O(log B (m + N)) amortized I/Os, where N is the size of the version being searched/updated, and m is the number of versions. – We solve the planar point location problem in linear space, taking optimal O(log B N) I/Os for point location queries, where N is the number of line segments specifying the partition of the plane. The pre-processing requires O((N/B) log M/B N) I/Os, where M is the size of the ‘inner ’ memory. 1