arXiv subjects

Shendan Jin

Publications and source records attributed to Shendan Jin.

3 recordsLinked to original sources

arXiv2024

Online Computation with Untrusted Advice

We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust if the advice is adversarial, and efficient is the advice is foolproof. We focus on four well-studied online problems, namely ski rental, online bidding, bin packing and list update. For ski rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved, whereas for bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or adversarial. More importantly, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm.

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arXiv2021

Online Maximum Matching with Recourse

We study the online maximum matching problem in a model in which the edges are associated with a known recourse parameter $k$. An online algorithm for this problem has to maintain a valid matching while edges of the underlying graph are presented one after the other. At any moment the algorithm can decide to include an edge into the matching or to exclude it, under the restriction that at most $k$ such actions per edge take place, where $k$ is typically a small constant. This problem was introduced and studied in the context of general online packing problems with recourse by Avitabile et al. [Information Processing Letters, 2013], whereas the special case $k=2$ was studied by Boyar et al. [WADS 2017]. In the first part of this paper we consider the edge arrival model, in which an arriving edge never disappears from the graph. Here, we first show an improved analysis on the performance of the algorithm AMP of Avitabile et al., by exploiting the structure of the matching problem. In addition, we show that the greedy algorithm has competitive ratio $3/2$ for every even $k$ and ratio $2$ for every odd $k$. Moreover, we present and analyze an improvement of the greedy algorithm which we call $L$-Greedy, and we show that for small values of $k$ it outperforms the algorithm AMP. In terms of lower bounds, we show that no deterministic algorithm better than $1+1/(k-1)$ exists, improving upon the known lower bound of $1+1/k$. The second part of the paper is devoted to the edge arrival/departure model, which is the fully dynamic variant of online matching with recourse. The analysis of $L$-Greedy and AMP carry through in this model; moreover we show a lower bound of $(k^2-3k+6) / (k^2-4k+7)$ for all even $k \ge 4$. For $k\in\{2,3\}$, the competitive ratio is $3/2$.

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arXiv2018

Best-of-two-worlds analysis of online search

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, intuitively, should have different performance in practice. Motivated by the above, in this work we introduce and study measures supplementary to competitive analysis in the context of search problems. In particular, we focus on the well-known problem of linear search, informally known as the cow-path problem, for which there is an infinite number of strategies that achieve an optimal competitive ratio equal to 9. We propose a measure that reflects the rate at which the line is being explored by the searcher, and which can be seen as an extension of the bijective ratio over an uncountable set of requests. Using this measure we show that a natural strategy that explores the line aggressively is optimal among all 9-competitive strategies. This provides, in particular, a strict separation from the competitively optimal doubling strategy, which is much more conservative in terms of exploration. We also provide evidence that this aggressiveness is requisite for optimality, by showing that any optimal strategy must mimic the aggressive strategy in its first few explorations.

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