Mathematics of String Spaces and Algorithmic Applications (09w5124)
Alberto Apostolico (Georgia Tech)
Gad Landau (University of Haifa)
Ian Munro (University of Waterloo)
Shan Muthukrishnan (Rutgers University)
Cenk Sahinalp (Simon Fraser University)
measures. We believe that a workshop devoted to the investigation of the mathematics of string spaces with specific emphasis on their relation to normed vector spaces such as $L_1$ and $L_2$ -for which there is a much better mathematical understanding- will be of considerable interest.
The main topics that will be covered by the proposed workshop will be: (1) embedding properties of string spaces, (2) approximating distances in string spaces, (3) indexibility of and efficient similarity search in string spaces, (4) sketching algorithms for strings and their applications in streaming and (5) applications of property testing methods for processing collections of strings. The workshop will also have discussions on potential applications of these mathematical results to more traditional algorithmic problems involving strings.
One of the main goals of the workshop is the identification of the key challenges and open problems related to mathematics of string spaces and their algorithmic applications. Here are a sample of interesting problems that will be discussed: (1) tight bounds on the volume of a ball of radius r in the string space (as a function of origin and alphabet size), (2) a poly-log d distortion embedding of edit distance to $L1$, (3) approximate or exact nearest neighbors data structures for strings under edit distance variants, (4) tightly approximating edit distance in near linear or sublinear time, (5) any lower bound on approximate randomized data structures for near or nearest neighbor search in metric spaces. We also hope to identify the most helpful tools available for such problems, developed specifically for string spaces or other domains.
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