虽然竞争分析已经是一个非常有用的在线算法质量的性能指标，它被认为是有时无法区分不同质量的算法在实践中。已经提出了一些替代措施，但是，除了少数例外，这些措施通常只适用于与之相关的在线问题。最近，发起了对在线算法的性能测量的系统研究[Boyar，Irani，Larsen：Eleventh International Algorithms and数据结构Symposium 2009]，首先关注简单的服务器问题。我们继续这项工作，通过研究一个根本不同的在线问题，在线搜索，特别是预订价格政策。这条工作线的目的是了解更多关于不同情况下各种绩效衡量标准的适用性以及不同衡量标准所强调的属性。我们研究了以下分析技术：竞争，相对最差顺序，双射，平均，相对区间，随机顺序和最大/最大。除了对这项工作得出结论外，我们还研究了测度对积分域与实值域的敏感性，并作为这项工作的一部分，推广了一些已知的性能测度。最后，我们建立了相对区间分析的第一个最优性证明。
英文摘要：
Though competitive analysis has been a very useful performance measure for the quality of online algorithms, it is recognized that it sometimes fails to distinguish between algorithms of different quality in practice. A number of alternative measures have been proposed, but, with a few exceptions, these have generally been applied only to the online problem they were developed in connection with. Recently, a systematic study of performance measures for online algorithms was initiated [Boyar, Irani, Larsen: Eleventh International Algorithms and Data Structures Symposium 2009], first focusing on a simple server problem. We continue this work by studying a fundamentally different online problem, online search, and the Reservation Price Policies in particular. The purpose of this line of work is to learn more about the applicability of various performance measures in different situations and the properties that the different measures emphasize. We investigate the following analysis techniques: Competitive, Relative Worst Order, Bijective, Average, Relative Interval, Random Order, and Max/Max. In addition to drawing conclusions on this work, we also investigate the measures' sensitivity to integral vs. real-valued domains, and as a part of this work, generalize some of the known performance measures. Finally, we have established the first optimality proof for Relative Interval Analysis.
We present an algorithm for computing upper bounds for the Online Bin Stretching Problem with a small number of bins and the resulting upper bounds for 4, 5 and 6 bins. This both demonstrates the possibility of using computer search for upper bounds on a fundamentally real-valued online problem and improves upon the best bounds know so far, some of which have remained unchanged since 2001.
We study the setting in which a mobile agent must locate a hidden target in a bounded or unbounded environment, with no information about the hider's position. In particular, we consider online search, in which the performance of the search strategy is evaluated by its worst case competitive ratio. We introduce a multi-criteria search problem in which the searcher has a budget on its allotted search time, and the objective is to design strategies that are competitively efficient, respect the budget, and maximize the total searched ground. We give analytically optimal strategies for the line an…
We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree. This model is based on a simple structure for decomposing graphs, previously known under several names including elimination trees, vertex rankings, and tubings. The model is equivalent to the classical binary search tree model exactly when the underlying tree is a path. We describe an online $O(\log \log n)$-competitive search tree data s…
Tiedemann, et al. [Proc. of WALCOM, LNCS 8973, 2015, pp.210-221] defined multi-objective online problems (as an online version of multi-objective optimization problems) and the competitive analysis for multi-objective online problems and showed that (1) with respect to the worst component competitive analysis, the online algorithm RPP-HIGH is best possible for the multi-objective time series search~problem; (2) with respect to the arithmetic mean component competitive analysis, the online algorithm RPP-MULT is best possible for the bi-objective time series search problem; (3) with respect to t…
The online search problem is a fundamental problem in finance. The numerous direct applications include searching for optimal prices for commodity trading and trading foreign currencies. In this paper, we analyze the advice complexity of this problem. In particular, we are interested in identifying the minimum amount of information needed in order to achieve a certain competitive ratio. We design an algorithm that reads b bits of advice and achieves a competitive ratio of (M/m)^(1/(2^b+1)) where M and m are the maximum and minimum price in the input. We also give a matching lower bound. Furthe…
Motivated by demand-responsive parking pricing systems we consider posted-price algorithms for the online metrical matching problem and the online metrical searching problem in a tree metric. Our main result is a poly-log competitive posted-price algorithm for online metrical searching.
We study an online version of the noisy binary search problem where feedback is generated by a non-stochastic adversary rather than perturbed by random noise. We reframe this as maintaining an accurate estimate for the median of an adversarial sequence of integers, $x_1, x_2, \dots$, in a model where each number $x_t$ can only be accessed through a single threshold query of the form ${1(x_t \leq q_t)}$. In this online comparison feedback model, we explore estimation of general sample statistics, providing robust algorithms for median, CDF, and mean estimation with nearly matching lower bounds.…
We consider the online search problem in which a server starting at the origin of a $d$-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which each point on the $d$-dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in $Ω(d)\cap O(d^{3/2})$.
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string matching is an efficient approach recently introduced in order to overcome the prohibitive space requirements of an index construction, on the one hand, and drastically reduce searching time for the online solutions, on the other hand. In this paper we present a new algorithm for the sampled string matching problem, based on a characters distance sampling approa…
In this paper we propose an online approximate k-nn graph building algorithm, which is able to quickly update a k-nn graph using a flow of data points. One very important step of the algorithm consists in using the current distributed graph to search for the neighbors of a new node. Hence we also propose a distributed partitioning method based on balanced k-medoids clustering, that we use to optimize the distributed search process. Finally, we present the improved sequential search procedure that is used inside each partition. We also perform an experimental evaluation of the different algorit…
In search problems, a mobile searcher seeks to locate a target that hides in some unknown position of the environment. Such problems are typically considered to be of an on-line nature, in that the input is unknown to the searcher, and the performance of a search strategy is usually analyzed by means of the standard framework of the competitive ratio, which compares the cost incurred by the searcher to an optimal strategy that knows the location of the target. However, one can argue that even for simple search problems, competitive analysis fails to distinguish between strategies which, intuit…
Near-Optimal Algorithms for Online Matrix Prediction
Technion - Israel Institute of Technology（以色列理工学院）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Hebrew University（希伯来大学）
在最近感兴趣的几个在线预测问题中，比较类由具有有界元素的矩阵组成。例如，在在线最大割问题中，比较类是表示给定图的割的矩阵，而在在线赌博中，比较类是表示n个团队的排列的矩阵。另一个重要的例子是在线协同过滤，其中广泛使用的比较类是具有小迹范数的矩阵集。在本文中，我们隔离矩阵的一个属性，我们称之为（beta，tau）-可分解性，并推导出一个有效的在线学习算法，享有遗憾界O*（sqrt（beta tau T））的所有问题，其中的比较类是由（beta，tau）-可分解矩阵。通过分析切割矩阵，三角矩阵和低迹范数矩阵的可分解性，我们获得了在线最大切割，在线赌博和在线协同过滤的近最佳遗憾界。特别是，这解决了Abernethy（2010）; Kleinberg et al（2010）提出的一个悬而未决的问题。最后，我们推导出这三个问题的下界，并表明我们的上界是最佳的对数因子。特别是，我们的在线协同过滤问题的下限解决了Shamir和Srebro（2011）提出的另一个开放问题。
The linear search problem, informally known as the cow path problem, is one of the fundamental problems in search theory. In this problem, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher, initially positioned at some specific point of the line called the root, must traverse the line so as to locate the target. The objective is to minimize the worst-case ratio of the distance traversed by the searcher to the distance of the target from the root, which is known as the competitive ratio of the search. In this work we study this problem in a settin…
CNRS（法国国家科学研究中心）；Sorbonne University（索邦大学）；University of Manitoba（曼尼托巴大学）
In the online (time-series) search problem, a player is presented with a sequence of prices which are revealed in an online manner. In the standard definition of the problem, for each revealed price, the player must decide irrevocably whether to accept or reject it, without knowledge of future prices (other than an upper and a lower bound on their extreme values), and the objective is to minimize the competitive ratio, namely the worst-case ratio between the maximum price in the sequence and the one selected by the player. The problem formulates several applications of decision-making in the f…
