A highly-efficient ANSI-C facility is described for intelligently comparing a query string with a series of database strings. The bipartite weighted matching approach taken tolerates ordering violations that are problematic for simple automaton or string edit distance methods---yet common in practice. The method is character and polygraph based and does not require that words are properly formed in a query. Database characters are processed at a rate of approximately 2.5 million per second using a 200MHz Pentium Pro processor. A subroutine-level API is described along with an simple executable utility supporting both command-line and Web interfaces. An optimized Web interface is also reported consisting of a daemon that preloads multiple databases, and a corresponding CGI stub. The daemon may be initiated manually or via inetd. Keywords: String Comparison/Similarity, Text/Database Search/Retrieval, Bipartite Matching/Assignment, Edit Distance. Both authors are with the NEC Research I...

We present efficient algorithms for finding a minimum cost perfect matching, and for solving the transportation problem in bipartite graphs, G = (Sinks [ Sources; Sinks 2 Sources), where jSinksj = n, jSourcesj = m, n m, and the cost function obeys the quadrangle inequality. First, we assume that all the sink points and all the source points lie on a curve that is homeomorphic to either a line or a circle and the cost function is given by the Euclidean distance along the curve. We present a linear time algorithm for the matching problem that is simpler than the algorithm of [KL75]. We generalize our method to solve the corresponding transportation problem in O((m+n) log(m +n)) time, improving on the best previously known algorithm of [KL75]. Next, we present an O(n log m)-time algorithm for minimum cost matching when the cost array is a bitonic Monge array. An example of this is when the sink points lie on one straight line and the source points lie on another straight line Finally...

Let S and T be two finite sets of points on the real line with |S| + |T | = n and |S| > |T |. The restriction scaffold assignment problem in computational biology assigns each point of S to a point of T such that the sum of all the assignment costs is minimized, with the constraint that every element of T must be assigned at least one element of S. The cost of assigning an element s i of S to an element t j of T is |s i - t j |, i.e., the distance between s i and t j . In 2003 Ben-Dor, Karp, Schwikowski and Shamir [2] published an O(n logn) time algorithm for this problem. Here we provide a counter-example to their algorithm and present a new algorithm that runs in O(n ) time, improving the best previous complexity of O(n ).

Musical rhythm is considered from the point of view of geometry.

Most shotgun sequencing projects undergo a long and costly phase of finishing, in which a partial assembly forms several contigs whose order, orientation and relative distance is unknown. We propose here a new technique that supplements the shotgun assembly data by experimentally simple and commonly used complete restriction digests of the target. By computationally combining information from the contig sequences and the fragment sizes measured for several different enzymes, we seek to form a "scaffold" on which the contigs will be placed in their correct orientation, order and distance. We give a heuristic search algorithm for solving the problem and report on promising preliminary simulation results. The key to the success of the search scheme is the very rapid solution of two time-critical subproblems that are solved to optimality in linear time.

Approximate string comparison and search is an important part of applications that range from natural language to the interpretation of DNA. This paper presents a bipartite weighted graph matching approach to these problems, based on the authors' linear time matching algorithms # . Our approach's tolerance to permutation of symbols or blocks, distinguishes it from the widely used edit distance and finite state machine methods. A close relationship with the earlier related `proximity comparison' method is established.

The restriction sca#old assignment problem takes as input two finite point sets S and T (with S containing more points than T ) and establishes a correspondence between points in S and points in T , such that each point in S maps to exactly one point in T , and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)- time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted).

Abstract. Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈ S to t ∈ T is equal to the distance between s and t. In this context, we provide an algorithm that determines a minimum-cost many-to-many matching in O(n log n) time, improving the previous best time complexity of O(n 2) for the same problem. 1.

Let S and T be two finite sets of points on the real line with |S| + |T | = n and |S| > |T |. We consider two distance measures between S and T that have applications in music information retrieval and computational biology: the surjection distance and the link distance. The former is called the restriction sca#old assignment problem in computational biology, and assigns each point of S to a point of T such that the sum of all the assignment costs is minimized, with the constraint that every element of T must be assigned at least one element of S. The cost of assigning an element s i of S to an element t j of T is |s i - t j |, i.e., the distance between s i and t j . In 2003 Ben-Dor, Karp, Schwikowski and Shamir [2] published an O(n log n) time algorithm for this problem.

Many problems concerning the theory and technology of rhythm, melody, and voice-leading are fundamentally geometric in nature. It is therefore not surprising that the field of computational geometry can contribute greatly to these problems. The interaction between computational geometry and music yields new insights into the theories of rhythm, melody, and voice-leading, as well as new problems for research in several areas, ranging from mathematics and computer science to music theory, music perception, and musicology. Recent results on the geometric and computational aspects of rhythm, melody, and voice-leading are reviewed, connections to established areas of computer science, mathematics, statistics, computational biology, and crystallography are pointed out, and new open problems are proposed. 1