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Documents authored by Bhawalkar, Kshipra


Document
Maximizing Revenue in the Presence of Intermediaries

Authors: Gagan Aggarwal, Kshipra Bhawalkar, Guru Guruganesh, and Andres Perlroth

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
We study the mechanism design problem of selling k items to unit-demand buyers with private valuations for the items. A buyer either participates directly in the auction or is represented by an intermediary, who represents a subset of buyers. Our goal is to design robust mechanisms that are independent of the demand structure (i.e. how the buyers are partitioned across intermediaries), and perform well under a wide variety of possible contracts between intermediaries and buyers. We first consider the case of k identical items where each buyer draws its private valuation for an item i.i.d. from a known λ-regular distribution. We construct a robust mechanism that, independent of the demand structure and under certain conditions on the contracts between intermediaries and buyers, obtains a constant factor of the revenue that the mechanism designer could obtain had she known the buyers' valuations. In other words, our mechanism’s expected revenue achieves a constant factor of the optimal welfare, regardless of the demand structure. Our mechanism is a simple posted-price mechanism that sets a take-it-or-leave-it per-item price that depends on k and the total number of buyers, but does not depend on the demand structure or the downstream contracts. Next we generalize our result to the case when the items are not identical. We assume that the item valuations are separable, i.e. v_{i j} = η_j v_i for buyer i and item j, with each private v_i drawn i.i.d. from a known λ-regular distribution. For this case, we design a mechanism that obtains at least a constant fraction of the optimal welfare, by using a menu of posted prices. This mechanism is also independent of the demand structure, but makes a relatively stronger assumption on the contracts between intermediaries and buyers, namely that each intermediary prefers outcomes with a higher sum of utilities of the subset of buyers represented by it.

Cite as

Gagan Aggarwal, Kshipra Bhawalkar, Guru Guruganesh, and Andres Perlroth. Maximizing Revenue in the Presence of Intermediaries. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 1:1-1:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{aggarwal_et_al:LIPIcs.ITCS.2022.1,
  author =	{Aggarwal, Gagan and Bhawalkar, Kshipra and Guruganesh, Guru and Perlroth, Andres},
  title =	{{Maximizing Revenue in the Presence of Intermediaries}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.1},
  URN =		{urn:nbn:de:0030-drops-155979},
  doi =		{10.4230/LIPIcs.ITCS.2022.1},
  annote =	{Keywords: Mechanism Design, Revenue Maximization, Posted Price Mechanisms}
}
Document
APPROX
Revenue Maximization in Transportation Networks

Authors: Kshipra Bhawalkar, Kostas Kollias, and Manish Purohit

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)


Abstract
We study the joint optimization problem of pricing trips in a transportation network and serving the induced demands by routing a fleet of available service vehicles to maximize revenue. Our framework encompasses applications that include traditional transportation networks (e.g., airplanes, buses) and their more modern counterparts (e.g., ride-sharing systems). We describe a simple combinatorial model, in which each edge in the network is endowed with a curve that gives the demand for traveling between its endpoints at any given price. We are supplied with a number of vehicles and a time budget to serve the demands induced by the prices that we set, seeking to maximize revenue. We first focus on a (preliminary) special case of our model with unit distances and unit time horizon. We show that this version of the problem can be solved optimally in polynomial time. Switching to the general case of our model, we first present a two-stage approach that separately optimizes for prices and routes, achieving a logarithmic approximation to revenue in the process. Next, using the insights gathered in the first two results, we present a constant factor approximation algorithm that jointly optimizes for prices and routes for the supply vehicles. Finally, we discuss how our algorithms can handle capacitated vehicles, impatient demands, and selfish (wage-maximizing) drivers.

Cite as

Kshipra Bhawalkar, Kostas Kollias, and Manish Purohit. Revenue Maximization in Transportation Networks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 26:1-26:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bhawalkar_et_al:LIPIcs.APPROX/RANDOM.2021.26,
  author =	{Bhawalkar, Kshipra and Kollias, Kostas and Purohit, Manish},
  title =	{{Revenue Maximization in Transportation Networks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{26:1--26:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.26},
  URN =		{urn:nbn:de:0030-drops-147197},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.26},
  annote =	{Keywords: Pricing, networks, approximation algorithms}
}
Document
Online Set Cover with Set Requests

Authors: Kshipra Bhawalkar, Sreenivas Gollapudi, and Debmalya Panigrahi

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)


Abstract
We consider a generic online allocation problem that generalizes the classical online set cover framework by considering requests comprising a set of elements rather than a single element. This problem has multiple applications in cloud computing, crowd sourcing, facility planning, etc. Formally, it is an online covering problem where each online step comprises an offline covering problem. In addition, the covering sets are capacitated, leading to packing constraints. We give a randomized algorithm for this problem that has a nearly tight competitive ratio in both objectives: overall cost and maximum capacity violation. Our main technical tool is an online algorithm for packing/covering LPs with nested constraints, which may be of interest in other applications as well.

Cite as

Kshipra Bhawalkar, Sreenivas Gollapudi, and Debmalya Panigrahi. Online Set Cover with Set Requests. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 64-79, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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@InProceedings{bhawalkar_et_al:LIPIcs.APPROX-RANDOM.2014.64,
  author =	{Bhawalkar, Kshipra and Gollapudi, Sreenivas and Panigrahi, Debmalya},
  title =	{{Online Set Cover with Set Requests}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{64--79},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.64},
  URN =		{urn:nbn:de:0030-drops-46883},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.64},
  annote =	{Keywords: Online Algorithms, Set Cover}
}
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