Showing papers by "Ming-Yang Kao published in 2005"

Complexities for Generalized Models of Self-Assembly

Abstract: In this paper, we study the complexity of self-assembly under models that are natural generalizations of the tile self-assembly model. In particular, we extend Rothemund and Winfree's study of the tile complexity of tile self-assembly [Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, Portland, OR, 2000, pp. 459--468]. They provided a lower bound of $\Omega(\frac{\log N}{\log\log N})$ on the tile complexity of assembling an $N\times N$ square for almost all N. Adleman et al. [Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, Heraklion, Greece, 2001, pp. 740--748] gave a construction which achieves this bound. We consider whether the tile complexity for self-assembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size $O(\sqrt{\log N})$ which assembles an $N\times N$ square in a model which allows flexible glue strength between nonequal glues. This result is matched for almost all N by a lower bound dictated by Kolmogorov complexity. For three other generalizations, we show that the $\Omega(\frac{\log N}{\log\log N})$ lower bound applies to $N\times N$ squares. At the same time, we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets. Specifically, for thin rectangles with length N and width k, we provide a tighter lower bound of $\Omega(\frac{N^{1/k}}{k})$ for the standard model, yet we also give a construction which achieves $O(\frac{\log N}{\log\log N})$ complexity in a model in which the temperature of the tile system is adjusted during assembly. We also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape; we show that this problem is NP-hard for three of the generalized models.

Towards truthful mechanisms for binary demand games: a general framework

Abstract: The family of Vickrey-Clarke-Groves (VCG) mechanisms is arguably the most celebrated achievement in truthful mechanism design. However, VCG mechanisms have their limitations. They only apply to optimization problems with a utilitarian (or affine) objective function, and their output should optimize the objective function. For many optimization problems, finding the optimal output is computationally intractable. If we apply VCG mechanisms to polynomial-time algorithms that approximate the optimal solution, the resulting mechanisms may no longer be truthful.In light of these limitations, it is useful to study whether we can design a truthful non-VCG payment scheme that is computationally tractable for a given allocation rule O. In this paper, we focus our attention on emphbinary demand games in which the agents' only available actions are to take part in the a game or not to. For these problems, we prove that a truthful mechanism M=(O, P) exists with a proper payment method P iff the allocation rule O satisfies a certain monotonicity property. We provide a general framework to design such P. We further propose several general composition-based techniques to compute P efficiently for various types of output. In particular, we show how P can be computed through "or/and" combinations, round-based combinations, and some more complex combinations of the outputs from subgames.

Fast Universalization of Investment Strategies

Abstract: A universalization of a parameterized investment strategy is an online algorithm whose average daily performance approaches that of the strategy operating with the optimal parameters determined offline in hindsight. We present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable. We present examples of common investment strategies that fit into our framework. The examples include both trading strategies that decide positions in individual stocks, and portfolio strategies that allocate wealth among multiple stocks. This work extends in a natural way Cover's universal portfolio work. We also discuss the runtime efficiency of universalization algorithms. While a straightforward implementation of our algorithms runs in time exponential in the number of parameters, we show that the efficient universal portfolio computation technique of Kalai and Vempala [Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, Redondo Beach, CA, 2000, pp. 486--491] involving the sampling of log-concave functions can be generalized to other classes of investment strategies, thus yielding provably good approximation algorithms in our framework.

Randomized fast design of short DNA words

Abstract: We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous work has extended results from coding theory to obtain bounds on code size for new biologically motivated constraints and has applied heuristic local search and genetic algorithm techniques for code design. This paper proposes a natural optimization formulation of the DNA code design problem in which the goal is to design n strings that satisfy a given set of constraints while minimizing the length of the strings. For multiple sets of constraints, we provide high-probability algorithms that run in time polynomial in n and any given constraint parameters, and output strings of length within a constant factor of the optimal. To the best of our knowledge, this work is the first to consider this type of optimization problem in the context of DNA code design.

Optimal Augmentation for Bipartite Componentwise Biconnectivity in Linear Time

Abstract: A graph is componentwise biconnected if every connected component either is an isolated vertex or is biconnected. We present a linear-time algorithm for the problem of adding the smallest number of edges to make a bipartite graph componentwise biconnected while preserving its bipartiteness. This algorithm has immediate applications for protecting sensitive information in statistical tables.

Average case analysis for tree labelling schemes

Abstract: We study how to label the vertices of a tree in such a way that we can decide the distance of two vertices in the tree given only their labels. For trees, Gavoille et al. [7] proved that for any such distance labelling scheme, the maximum label length is at least ${1 \over 8} {\rm log}^{2} n - O({\rm log} n)$ bits. They also gave a separator-based labelling scheme that has the optimal label length ${\it \Theta}({\rm log} {n} \cdot {\rm log}(H_{n}(T)))$, where Hn(T) is the height of the tree. In this paper, we present two new distance labelling schemes that not only achieve the optimal label length ${\it \Theta}({\rm log} n \cdot {\rm log} (H_{n}(T)))$, but also have a much smaller expected label length under certain tree distributions. With these new schemes, we also can efficiently find the least common ancestor of any two vertices based on their labels only.