arXiv subjects

Agnieszka Tatarczuk

Publications and source records attributed to Agnieszka Tatarczuk.

4 recordsLinked to original sources

arXiv2026

Pure Tail Constraints for Online Problems

Controlling tail risk is an important objective in online optimization, and recently it has been studied in the context of competitive analysis. Continuing this line of research, we investigate pure tail constraints, which capture the tradeoff between expected and worst-case competitiveness. For two fundamental search problems, online bidding and line search, we derive the Pareto-optimal frontiers of this tradeoff. We then investigate another classic problem, TCP acknowledgment, which has structure similar to the iterated ski rental problem. There, we construct an algorithm whose tradeoff coincides with the known Pareto-optimal tradeoff for ski rental. The lower bounds for this problem are substantially more involved as the problem exhibits adaptive structure: an online algorithm observes requests of the adversary (packet arrivals) and may adaptively adjust its actions (acknowledgments) on this basis. We emphasize that all previous work on tail risk in the context of competitive analysis was restricted to non-adaptive problems, where the feedback given to an algorithm was essentially limited to a binary indicator of whether the algorithm has succeeded or not. Nonetheless, we identify a set of constraints implied by tail bounds in this adaptive setting, and show that they imply a nontrivial lower bound on the TCP acknowledgment problem.

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arXiv2026

Online Bisection with Ring Demands

The online bisection problem requires maintaining a dynamic partition of $n$ nodes into two equal-sized clusters. Requests arrive sequentially as node pairs. If the nodes lie in different clusters, the algorithm pays unit cost. After each request, the algorithm may migrate nodes between clusters at unit cost per node. This problem models datacenter resource allocation where virtual machines must be assigned to servers, balancing communication costs against migration overhead. We study the variant where requests are restricted to edges of a ring network, an abstraction of ring-allreduce patterns in distributed machine learning. Despite this restriction, the problem remains challenging with an $Ω(n)$ deterministic lower bound. We present a randomized algorithm achieving $O(\varepsilon^{-3} \cdot \log^2 n)$ competitive ratio using resource augmentation that allows clusters of size at most $(3/4 + \varepsilon) \cdot n$. Our approach formulates the problem as a metrical task system with a restricted state space. By limiting the number of cut-edges (i.e., ring edges between clusters) to at most $2k$, where $k = Θ(1/\varepsilon)$, we reduce the state space from exponential to polynomial (i.e., $n^{O(k)}$). The key technical contribution is proving that this restriction increases cost by only a factor of $O(k)$. Our algorithm follows by applying the randomized MTS solution of Bubeck et al. [SODA 2019]. The best result to date for bisection with ring demands is the $O(n \cdot \log n)$-competitive deterministic online algorithm of Rajaraman and Wasim [ESA 2024] for the general setting. While prior work for ring-demands by Räcke et al. [SPAA 2023] achieved $O(\log^3 n)$ for multiple clusters, their approach employs a resource augmentation factor of $2+\varepsilon$, making it inapplicable to bisection.

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arXiv2025

A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs

We consider the List Update problem where the cost of each swap is assumed to be 1. This is in contrast to the ``standard'' model, in which an algorithm is allowed to swap the requested item with previous items for free. We construct an online algorithm Full-Or-Partial-Move (FPM), whose competitive ratio is at most $3.3904$, improving over the previous best known bound of $4$.

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arXiv2023

An Improved Deterministic Algorithm for the Online Min-Sum Set Cover Problem

We study the online variant of the Min-Sum Set Cover (MSSC) problem, a generalization of the well-known list update problem. In the MSSC problem, an algorithm has to maintain the time-varying permutation of the list of $n$ elements, and serve a sequence of requests $R_1, R_2, \dots, R_t, \dots$. Each $R_t$ is a subset of elements of cardinality at most $r$. For a requested set $R_t$, an online algorithm has to pay the cost equal to the position of the first element from $R_t$ on its list. Then, it may arbitrarily permute its list, paying the number of swapped adjacent element pairs. We present the first constructive deterministic algorithm for this problem, whose competitive ratio does not depend on $n$. Our algorithm is $O(r^2)$-competitive, which beats both the existential upper bound of $O(r^4)$ by Bienkowski and Mucha [AAAI '23] and the previous constructive bound of $O(r^{3/2} \cdot \sqrt{n})$ by Fotakis et al. [ICALP '20]. Furthermore, we show that our algorithm attains an asymptotically optimal competitive ratio of $O(r)$ when compared to the best fixed permutation of elements.

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