4 Search Results for "Oosterwijk, Tim"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.86
The Secretary Problem with Predictions and a Chosen Order

Authors: Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023). In this variant, the decision-maker has access to machine-learned predictions of candidate values in advance. The key challenge is to balance consistency and robustness: when the predictions are accurate, the algorithm should hire a near-best secretary; however, if they are inaccurate, the algorithm should still achieve a bounded competitive ratio. We consider both the standard Random Order Secretary Problem (ROSP), where candidates arrive in a uniform random order, and a more natural model in the learning-augmented setting, where the decision-maker can choose the arrival order based on the predicted candidate values. This model, which we call the Chosen Order Secretary Problem (COSP), can capture scenarios such as an interview schedule that is set by the decision-maker. We propose a novel algorithm that applies to both ROSP and COSP. Building on the approach of Fujii and Yoshida, our method switches from fully trusting predictions to a threshold-based rule when a large deviation of a prediction is observed. Importantly, unlike the algorithm of Fujii and Yoshida, our algorithm uses randomization as part of its decision logic. We show that if ε ∈ [0,1] denotes the maximum multiplicative prediction error, then for ROSP our algorithm achieves competitive ratio max {0.221, (1-ε)/(1+ε)}, improving on a previous bound of max {0.215, (1-ε)/(1+ε)} due to Fujii and Yoshida [Fujii and Yoshida, 2023]. For COSP, our algorithm achieves max {0.262, (1-ε)/(1+ε)}. This surpasses a 0.25 upper bound on the worst-case competitive ratio that applies to the approach of Fujii and Yoshida, and gets closer to the classical secretary benchmark of 1/e ≈ 0.368, which is an upper bound for any algorithm. Our result for COSP highlights the benefit of integrating predictions with arrival-order control in online decision-making.
Cite as

Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco. The Secretary Problem with Predictions and a Chosen Order. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 86:1-86:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karisani_et_al:LIPIcs.ITCS.2026.86,
  author =	{Karisani, Helia and Daneshvaramoli, Mohammadreza and Beyhaghi, Hedyeh and Hajiesmaili, Mohammad and Musco, Cameron},
  title =	{{The Secretary Problem with Predictions and a Chosen Order}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{86:1--86:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.86},
  URN =		{urn:nbn:de:0030-drops-253734},
  doi =		{10.4230/LIPIcs.ITCS.2026.86},
  annote =	{Keywords: Secretary problem, learning-augmented algorithms, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.52
Beating Competitive Ratio 4 for Graphic Matroid Secretary

Authors: Kiarash Banihashem, MohammadTaghi Hajiaghayi, Dariusz R. Kowalski, Piotr Krysta, Danny Mittal, and Jan Olkowski

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
One of the classic problems in online decision-making is the secretary problem, where the goal is to hire the best secretary out of n rankable applicants or, in a natural extension, to maximize the probability of selecting the largest number from a sequence arriving in random order. Many works have considered generalizations of this problem where one can accept multiple values subject to a combinatorial constraint. The seminal work of Babaioff, Immorlica, Kempe, and Kleinberg (SODA'07, JACM'18) proposed the matroid secretary conjecture, suggesting that there exists an O(1)-competitive algorithm for the matroid constraint, and many works since have attempted to obtain algorithms for both general matroids and specific classes of matroids. The ultimate goal of these results is to obtain an e-competitive algorithm, and the strong matroid secretary conjecture states that this is possible for general matroids. One of the most important classes of matroids is the graphic matroid, where a set of edges in a graph is deemed independent if it contains no cycle. Given the rich combinatorial structure of graphs, obtaining algorithms for these matroids is often seen as a good first step towards solving the problem for general matroids. For matroid secretary, Babaioff et al. (SODA'07, JACM'18) first studied graphic matroid case and obtained a 16-competitive algorithm. Subsequent works have improved the competitive ratio, most recently to 4 by Soto, Turkieltaub, and Verdugo (SODA'18). In this paper, we break the 4-competitive barrier for the problem, obtaining a new algorithm with a competitive ratio of 3.95. For the special case of simple graphs (i.e., graphs that do not contain parallel edges) we further improve this to 3.77. Intuitively, solving the problem for simple graphs is easier as they do not contain cycles of length two. A natural question that arises is whether we can obtain a ratio arbitrarily close to e by assuming the graph has a large enough girth. We answer this question affirmatively, proving that one can obtain a competitive ratio arbitrarily close to e even for constant values of girth, providing further evidence for the strong matroid secretary conjecture. We further show that this bound is tight: for any constant g, one cannot obtain a competitive ratio better than e even if we assume that the input graph has girth at least g. To our knowledge, such a bound was not previously known even for simple graphs.
Cite as

Kiarash Banihashem, MohammadTaghi Hajiaghayi, Dariusz R. Kowalski, Piotr Krysta, Danny Mittal, and Jan Olkowski. Beating Competitive Ratio 4 for Graphic Matroid Secretary. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 52:1-52:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ESA.2025.52,
  author =	{Banihashem, Kiarash and Hajiaghayi, MohammadTaghi and Kowalski, Dariusz R. and Krysta, Piotr and Mittal, Danny and Olkowski, Jan},
  title =	{{Beating Competitive Ratio 4 for Graphic Matroid Secretary}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{52:1--52:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.52},
  URN =		{urn:nbn:de:0030-drops-245205},
  doi =		{10.4230/LIPIcs.ESA.2025.52},
  annote =	{Keywords: online algorithms, graphic matroids, secretary problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.86
Exact and Approximation Algorithms for Routing a Convoy Through a Graph

Authors: Martijn van Ee, Tim Oosterwijk, René Sitters, and Andreas Wiese

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
We study routing problems of a convoy in a graph, generalizing the shortest path problem (SPP), the travelling salesperson problem (TSP), and the Chinese postman problem (CPP) which are all well-studied in the classical (non-convoy) setting. We assume that each edge in the graph has a length and a speed at which it can be traversed and that our convoy has a given length. While the convoy moves through the graph, parts of it can be located on different edges. For safety requirements, at all time the whole convoy needs to travel at the same speed which is dictated by the slowest edge on which currently a part of the convoy is located. For Convoy-SPP, we give a strongly polynomial time exact algorithm. For Convoy-TSP, we provide an O(log n)-approximation algorithm and an O(1)-approximation algorithm for trees. Both results carry over to Convoy-CPP which - maybe surprisingly - we prove to be NP-hard in the convoy setting. This contrasts the non-convoy setting in which the problem is polynomial time solvable.
Cite as

Martijn van Ee, Tim Oosterwijk, René Sitters, and Andreas Wiese. Exact and Approximation Algorithms for Routing a Convoy Through a Graph. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 86:1-86:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vanee_et_al:LIPIcs.MFCS.2023.86,
  author =	{van Ee, Martijn and Oosterwijk, Tim and Sitters, Ren\'{e} and Wiese, Andreas},
  title =	{{Exact and Approximation Algorithms for Routing a Convoy Through a Graph}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{86:1--86:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.86},
  URN =		{urn:nbn:de:0030-drops-186205},
  doi =		{10.4230/LIPIcs.MFCS.2023.86},
  annote =	{Keywords: approximation algorithms, convoy routing, shortest path problem, traveling salesperson problem}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.4
Atomic Splittable Flow Over Time Games

Authors: Antonia Adamik and Leon Sering

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
In an atomic splittable flow over time game, finitely many players route flow dynamically through a network, in which edges are equipped with transit times, specifying the traversing time, and with capacities, restricting flow rates. Infinitesimally small flow particles controlled by the same player arrive at a constant rate at the player’s origin and the player’s goal is to maximize the flow volume that arrives at the player’s destination within a given time horizon. Here, the flow dynamics are described by the deterministic queuing model, i.e., flow of different players merges perfectly, but excessive flow has to wait in a queue in front of the bottle-neck. In order to determine Nash equilibria in such games, the main challenge is to consider suitable definitions for the players' strategies, which depend on the level of information the players receive throughout the game. For the most restricted version, in which the players receive no information on the network state at all, we can show that there is no Nash equilibrium in general, not even for networks with only two edges. However, if the current edge congestions are provided over time, the players can adapt their route choices dynamically. We show that a profile of those strategies always lead to a unique feasible flow over time. Hence, those atomic splittable flow over time games are well-defined. For parallel-edge networks Nash equilibria exists and the total flow arriving in time equals the value of a maximum flow over time leading to a price of anarchy of 1.
Cite as

Antonia Adamik and Leon Sering. Atomic Splittable Flow Over Time Games. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{adamik_et_al:LIPIcs.SAND.2022.4,
  author =	{Adamik, Antonia and Sering, Leon},
  title =	{{Atomic Splittable Flow Over Time Games}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.4},
  URN =		{urn:nbn:de:0030-drops-159462},
  doi =		{10.4230/LIPIcs.SAND.2022.4},
  annote =	{Keywords: Flows Over Time, Deterministic Queuing, Atomic Splittable Games, Equilibria, Traffic, Cooperation}
}
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