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DOI: 10.4230/LIPIcs.ITCS.2024.84

Budget-Feasible Mechanism Design: Simpler, Better Mechanisms and General Payment Constraints

Authors: Rian Neogi, Kanstantsin Pashkovich, and Chaitanya Swamy

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

In budget-feasible mechanism design, a buyer wishes to procure a set of items of maximum value from self-interested rational players. We are given an item-set U and a nonnegative valuation function v: 2^U ↦ ℝ_+. Each item e is held by a player who incurs a private cost c_e for supplying item e. The goal is to devise a truthful mechanism such that the total payment made to the players is at most some given budget B, and the value of the set returned is a good approximation to OPT: = max {v(S): c(S) ≤ B, S ⊆ U}. We call such a mechanism a budget-feasible mechanism. More generally, there may be additional side constraints requiring that the set returned lies in some downwards-monotone family ℐ ⊆ 2^U. Budget-feasible mechanisms have been widely studied, but there are still significant gaps in our understanding of these mechanisms, both in terms of what kind of oracle access to the valuation is required to obtain good approximation ratios, and the best approximation ratio that can be achieved. We substantially advance the state of the art of budget-feasible mechanisms by devising mechanisms that are simpler, and also better, both in terms of requiring weaker oracle access and the approximation factors they obtain. For XOS valuations, we devise the first polytime O(1)-approximation budget-feasible mechanism using only demand oracles, and also significantly improve the approximation factor. For subadditive valuations, we give the first explicit construction of an O(1)-approximation mechanism, where previously only an existential result was known. We also introduce a fairly rich class of mechanism-design problems that we dub using the umbrella term generalized budget-feasible mechanism design, which allow one to capture payment constraints that are much-more nuanced than a single constraint on the total payment doled out. We demonstrate the versatility of our ideas by showing that our constructions can be adapted to yield approximation guarantees in such general settings as well. A prominent insight to emerge from our work is the usefulness of a property called nobossiness, which allows us to nicely decouple the truthfulness + approximation, and budget-feasibility requirements. Some of our constructions can be viewed as reductions showing that an O(1)-approximation budget-feasible mechanism can be obtained provided we have a (randomized) truthful mechanism satisfying nobossiness that returns a (random) feasible set having (expected) value Ω(OPT).

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Rian Neogi, Kanstantsin Pashkovich, and Chaitanya Swamy. Budget-Feasible Mechanism Design: Simpler, Better Mechanisms and General Payment Constraints. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 84:1-84:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{neogi_et_al:LIPIcs.ITCS.2024.84,
  author =	{Neogi, Rian and Pashkovich, Kanstantsin and Swamy, Chaitanya},
  title =	{{Budget-Feasible Mechanism Design: Simpler, Better Mechanisms and General Payment Constraints}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{84:1--84:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.84},
  URN =		{urn:nbn:de:0030-drops-196128},
  doi =		{10.4230/LIPIcs.ITCS.2024.84},
  annote =	{Keywords: Algorithmic mechanism design, Approximation algorithms, Budget-feasible mechanisms}
}

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DOI: 10.4230/LIPIcs.MFCS.2020.75

On the Parameterized Complexity of Deletion to ℋ-Free Strong Components

Authors: Rian Neogi, M. S. Ramanujan, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract

Directed Feedback Vertex Set (DFVS) is a fundamental computational problem that has received extensive attention in parameterized complexity. In this paper, we initiate the study of a wide generalization, the ℋ-SCC Deletion problem. Here, one is given a digraph D, an integer k and the objective is to decide whether there is a vertex set of size at most k whose deletion leaves a digraph where every strong component excludes graphs in the fixed finite family ℋ as (not necessarily induced) subgraphs. When ℋ comprises only the digraph with a single arc, then this problem is precisely DFVS. Our main result is a proof that this problem is fixed-parameter tractable parameterized by the size of the deletion set if ℋ only contains rooted graphs or if ℋ contains at least one directed path. Along with generalizing the fixed-parameter tractability result for DFVS, our result also generalizes the recent results of Göke et al. [CIAC 2019] for the 1-Out-Regular Vertex Deletion and Bounded Size Strong Component Vertex Deletion problems. Moreover, we design algorithms for the two above mentioned problems, whose running times are better and match with the best bounds for DFVS, without using the heavy machinery of shadow removal as is done by Göke et al. [CIAC 2019].

Cite as

Rian Neogi, M. S. Ramanujan, Saket Saurabh, and Roohani Sharma. On the Parameterized Complexity of Deletion to ℋ-Free Strong Components. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{neogi_et_al:LIPIcs.MFCS.2020.75,
  author =	{Neogi, Rian and Ramanujan, M. S. and Saurabh, Saket and Sharma, Roohani},
  title =	{{On the Parameterized Complexity of Deletion to ℋ-Free Strong Components}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{75:1--75:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.75},
  URN =		{urn:nbn:de:0030-drops-127444},
  doi =		{10.4230/LIPIcs.MFCS.2020.75},
  annote =	{Keywords: Directed Cut Problems, Fixed-parameter Tractability, DFVS}
}

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Budget-Feasible Mechanism Design: Simpler, Better Mechanisms and General Payment Constraints

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On the Parameterized Complexity of Deletion to ℋ-Free Strong Components

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