Solving problems in P using correlated instances
| Autor: | Holden, Dhiraj |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Diplomová práce |
| Popis: | Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017. Cataloged from PDF version of thesis. Includes bibliographical references (page 39). Instances of computational problems do not exist in isolation. Rather, multiple and correlated instances of the same problem arise naturally in the real world. The challenge is how to gain computationally from correlations when they can be found. [DGH, ITCS 20151 showed that significant computational gains can be made by having access to auxiliary instances which are correlated with the primary problem instance via the solution space. Here, we set out to study the impact of having access to correlated instances on the complexity of polynomial time problems. Namely, for a problem P that is conjectured to require time n[superscript c] for c > 0, we ask whether access to a few instances of P that are correlated in some natural way can be used to solve P on one of them (the designated "primary instance") faster than the conjectured lower bound of nc. We focus our attention on a number of problems: the Longest Common Subsequence (LCS), the minimum Edit Distance between sequences, and the Dynamic Time Warping Distance (DTWD) of curves, for which the best known algorithms achieve Ō(n² ) runtime via dynamic programming. These problems form an interesting case in point to study, as it has been shown that a O(n[superscript 2-[epsilon]]) time algorithm for a worst-case instance would imply improved algorithms for a host of other problems as well as disprove complexity hypotheses such as the Strong Exponential Time Hypothesis. We show how to use access to a logarithmic number of auxiliary correlated instances, to design novel o(n² ) time algorithms for LCS, EDIT, DTWD, and more generally improved algorithms for computing any tuple-based similarity measure - a generalization which we define on strings. Our results hold for several correlation models between the primary and the auxiliary instances. In the most general correlation model we address, we assume that the primary instance is a worst-case instance and the auxiliary instances are chosen with uniform distribution subject to the constraint that their allignments are [epsilon]-correlated with the optimal allignment of the primary instance. by Dhiraj Holden. S.M. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
|