4 Search Results for "Rohatgi, Dhruv"

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.ITCS.2025.81
Online Balanced Allocation of Dynamic Components

Authors: Rajmohan Rajaraman and Omer Wasim

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We introduce Online Balanced Allocation of Dynamic Components (OBADC), a problem motivated by the practical challenge of dynamic resource allocation for large-scale distributed applications. In OBADC, we need to allocate a dynamic set of at most k𝓁 vertices (representing processes) in 𝓁 > 0 clusters. We consider an over-provisioned setup in which each cluster can hold at most k(1+ε) vertices, for an arbitrary constant ε > 0. The communication requirements among the vertices are modeled by the notion of a dynamically changing component, which is a subset of vertices that need to be co-located in the same cluster. At each time t, a request r_t of one of the following types arrives: 1) insertion of a vertex v forming a singleton component v at unit cost. 2) merge of (u,v) requiring that the components containing u and v be merged and co-located thereafter. 3) deletion of an existing vertex v at zero cost. Before serving any request, an algorithm can migrate vertices from one cluster to another, at a unit migration cost per vertex. We seek an online algorithm to minimize the total migration cost incurred for an arbitrary request sequence σ = (r_t)_{t > 0}, while simultaneously minimizing the number of clusters utilized. We analyze competitiveness with respect to an optimal clairvoyant offline algorithm with identical (over-provisioned) capacity constraints. We give an O(log k)-competitive algorithm for OBADC, and a matching lower-bound. The number of clusters utilized by our algorithm is always within a (2+ε) factor of the minimum. Furthermore, in a resource augmented setting where the optimal offline algorithm is constrained to capacity k per cluster, our algorithm obtains O(log k) competitiveness and utilizes a number of clusters within (1+ε) factor of the minimum. We also consider OBADC in the context of machine-learned predictions, where for each newly inserted vertex v at time t: i) with probability η > 0, the set of vertices (that exist at time t) in the component of v is revealed and, ii) with probability 1-η, no information is revealed. For OBADC with predictions, we give a O(1)-consistent and O(min(log 1/(η), log k))-robust algorithm.
Cite as

Rajmohan Rajaraman and Omer Wasim. Online Balanced Allocation of Dynamic Components. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 81:1-81:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rajaraman_et_al:LIPIcs.ITCS.2025.81,
  author =	{Rajaraman, Rajmohan and Wasim, Omer},
  title =	{{Online Balanced Allocation of Dynamic Components}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{81:1--81:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.81},
  URN =		{urn:nbn:de:0030-drops-227090},
  doi =		{10.4230/LIPIcs.ITCS.2025.81},
  annote =	{Keywords: online algorithms, competitive ratio, algorithms with predictions}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.54
New Approximation Algorithms for Touring Regions

Authors: Benjamin Qi and Richard Qi

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We analyze the touring regions problem: find a (1+ε)-approximate Euclidean shortest path in d-dimensional space that starts at a given starting point, ends at a given ending point, and visits given regions R₁, R₂, R₃, … , R_n in that order. Our main result is an O (n/√ε log{1/ε} + 1/ε)-time algorithm for touring disjoint disks. We also give an O(min(n/ε, n²/√ε))-time algorithm for touring disjoint two-dimensional convex fat bodies. Both of these results naturally generalize to larger dimensions; we obtain O(n/{ε^{d-1}} log²1/ε + 1/ε^{2d-2}) and O(n/ε^{2d-2})-time algorithms for touring disjoint d-dimensional balls and convex fat bodies, respectively.
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Benjamin Qi and Richard Qi. New Approximation Algorithms for Touring Regions. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{qi_et_al:LIPIcs.SoCG.2023.54,
  author =	{Qi, Benjamin and Qi, Richard},
  title =	{{New Approximation Algorithms for Touring Regions}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.54},
  URN =		{urn:nbn:de:0030-drops-179047},
  doi =		{10.4230/LIPIcs.SoCG.2023.54},
  annote =	{Keywords: shortest paths, convex bodies, fat objects, disks}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.12
Conditional Hardness of Earth Mover Distance

Authors: Dhruv Rohatgi

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
The Earth Mover Distance (EMD) between two sets of points A, B subseteq R^d with |A| = |B| is the minimum total Euclidean distance of any perfect matching between A and B. One of its generalizations is asymmetric EMD, which is the minimum total Euclidean distance of any matching of size |A| between sets of points A,B subseteq R^d with |A| <= |B|. The problems of computing EMD and asymmetric EMD are well-studied and have many applications in computer science, some of which also ask for the EMD-optimal matching itself. Unfortunately, all known algorithms require at least quadratic time to compute EMD exactly. Approximation algorithms with nearly linear time complexity in n are known (even for finding approximately optimal matchings), but suffer from exponential dependence on the dimension. In this paper we show that significant improvements in exact and approximate algorithms for EMD would contradict conjectures in fine-grained complexity. In particular, we prove the following results: - Under the Orthogonal Vectors Conjecture, there is some c>0 such that EMD in Omega(c^{log^* n}) dimensions cannot be computed in truly subquadratic time. - Under the Hitting Set Conjecture, for every delta>0, no truly subquadratic time algorithm can find a (1 + 1/n^delta)-approximate EMD matching in omega(log n) dimensions. - Under the Hitting Set Conjecture, for every eta = 1/omega(log n), no truly subquadratic time algorithm can find a (1 + eta)-approximate asymmetric EMD matching in omega(log n) dimensions.
Cite as

Dhruv Rohatgi. Conditional Hardness of Earth Mover Distance. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rohatgi:LIPIcs.APPROX-RANDOM.2019.12,
  author =	{Rohatgi, Dhruv},
  title =	{{Conditional Hardness of Earth Mover Distance}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.12},
  URN =		{urn:nbn:de:0030-drops-112270},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.12},
  annote =	{Keywords: Earth Mover Distance, Hardness of Approximation, Fine-Grained Complexity}
}
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