Approximating the Distortion
نویسندگان
چکیده
Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demonstrating that, when the distortion is large, it is hard to approximate within large factors, even for 1-dimensional point sets. We also introduce additive distortion, and show that it can be easily approximated within a factor of two.
منابع مشابه
Optimum Quantization and Its Applications
Minimum sums of moments or, equivalently, distorsion of optimum quantizers play an important role in several branches of mathematics. Fejes Tóth’s inequality for sums of moments in the plane and Zador’s asymptotic formula for minimum distortion in Euclidean d-space are the first precise pertinent results in dimension d ≥ 2. In this article these results are generalized in the form of asymptotic...
متن کاملApproximating Optimal Social Choice under Metric Preferences
We examine the quality of social choice mechanisms using a utilitarian view, in which all of the agents have costs for each of the possible alternatives. While these underlying costs determine what the optimal alternative is, they may be unknown to the social choice mechanism; instead the mechanism must decide on a good alternative based only on the ordinal preferences of the agents which are i...
متن کاملConstant Approximation Algorithms for Embedding Graph Metrics into Trees and Outerplanar Graphs
In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu, Indyk, and Sidiropoulos (2007) and Bǎdoiu, Demaine, Hajiaghayi, Sidiropoulos, and Zadimoghaddam (2008)). We also present a constant factor algorithm for approximati...
متن کاملA note on approximating snowflake metrics by trees
prove that the tree construction of Fakcharoenphol, Rao, and Talwar [2] can be used to approximate snowflake metrics by trees with expected distortion bounded independently of the size of the metric space. The constant of distortion we derive depends linearly on the dimension of the metric space. We also present an algorithm for building a single tree whose cost is linear in the problem size. A...
متن کاملIntegrated Project Member of the FET Proactive Initiative Complex Systems DELIS-TR-0171 Approximating the Distortion
Kenyon et al. (STOC 04) compute the distortion between one-dimensional finite point sets when the distortion is small; Papadimitriou and Safra (SODA 05) show that the problem is NP-hard to approximate within a factor of 3, albeit in 3 dimensions. We solve an open problem in these two papers by demonstrating that, when the distortion is large, it is hard to approximate within large factors, even...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005