13 Search Results for "Moulin, Hervé"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.38
Fairness and Efficiency in Two-Sided Matching Markets

Authors: Pallavi Jain, Palash Jha, and Shubham Solanki

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We propose a new fairness notion, motivated by the practical challenge of allocating teaching assistants (TAs) to courses in a department. Each course requires a certain number of TAs and each TA has preferences over the courses they want to assist. Similarly, each course instructor has preferences over the TAs who applied for their course. We demand fairness and efficiency for both sides separately, giving rise to the following criteria: (i) every course gets the required number of TAs and the average utility of the assigned TAs meets a threshold; (ii) the allocation of courses to TAs is envy-free, where a TA envies another TA if the former prefers the latter’s course and has a higher or equal grade in that course. Note that the definition of envy-freeness here differs from the one in the literature, and we call it merit-based envy-freeness. We show that the problem of finding a merit-based envy-free and efficient matching is NP-hard even for very restricted settings, such as two courses and uniform valuations; constant degree, constant capacity of TAs for every course, valuations in the range {0,1,2,3}, identical valuations from TAs, and even more. To find tractable results, we consider some restricted instances, such as, strict valuation of TAs for courses, the difference between the number of positively valued TAs for a course and the capacity, the number of positively valued TAs/courses, types of valuation functions, and obtained some polynomial-time solvable cases, showing the contrast with intractable results. We further studied the problem in the paradigm of parameterized algorithms and designed some exact and approximation algorithms.
Cite as

Pallavi Jain, Palash Jha, and Shubham Solanki. Fairness and Efficiency in Two-Sided Matching Markets. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jain_et_al:LIPIcs.FSTTCS.2025.38,
  author =	{Jain, Pallavi and Jha, Palash and Solanki, Shubham},
  title =	{{Fairness and Efficiency in Two-Sided Matching Markets}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.38},
  URN =		{urn:nbn:de:0030-drops-251186},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.38},
  annote =	{Keywords: Fair Matching, Envy-Freeness, Efficiency}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.15
Extending EFX Allocations to Further Multi-Graph Classes

Authors: Umang Bhaskar and Yeshwant Pandit

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The existence of EFX allocations is one of the most significant open questions in fair division. Recent work by Christodoulou, Fiat, Koutsoupias, and Sgouritsa ("Fair allocation in graphs," EC 2023) establishes the existence of EFX allocations for graphical valuations, when agents are vertices in a graph, items are edges, and each item has zero value for all agents other than those at its endpoints. Thus, in this setting, each good has non-zero value for at most two agents, and there is at most one good valued by any pair of agents. This marks one of the few cases when an exact and complete EFX allocation is known to exist for more than three agents. In this work, we partially extend these results to multi-graphs, when each pair of vertices can have more than one edge between them. The existence of EFX allocations in multi-graphs is a natural open question given their existence in simple graphs. We show that EFX allocations exist, and can be computed in polynomial time, for agents with cancelable valuations in the following cases: (i) bipartite multi-graphs, (ii) multi-trees with monotone valuations, and (iii) multi-graphs with girth (2t-1), where t is the chromatic number of the multi-graph. The existence of EFX in cycle multi-graphs follows from (i), (iii), and the known existence of EFX for three agents.
Cite as

Umang Bhaskar and Yeshwant Pandit. Extending EFX Allocations to Further Multi-Graph Classes. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhaskar_et_al:LIPIcs.FSTTCS.2025.15,
  author =	{Bhaskar, Umang and Pandit, Yeshwant},
  title =	{{Extending EFX Allocations to Further Multi-Graph Classes}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-250958},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.15},
  annote =	{Keywords: Fair Division, EFX, Multi-graphs}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.29
Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division

Authors: Ajaykrishnan E S and Daniel Lokshtanov

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent’s share. Focusing on agents with additive valuations, we show that the problem remains computationally hard when parameterized by p and the number of agents. This result holds even for star graphs and with the input numbers given in unary representation, thereby resolving an open problem posed by Gahlawat and Zehavi (FSTTCS 2023). In stark contrast, we show that if one is willing to tolerate even the slightest amount of envy, then the problem becomes efficient with respect to the natural parameters. Specifically, we design an Efficient Parameterized Approximation Scheme parameterized by p and the number of agent types. Our algorithm works on general graphs and remains efficient even when the input numbers are provided in binary representation.
Cite as

Ajaykrishnan E S and Daniel Lokshtanov. Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{es_et_al:LIPIcs.FSTTCS.2025.29,
  author =	{E S, Ajaykrishnan and Lokshtanov, Daniel},
  title =	{{Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.29},
  URN =		{urn:nbn:de:0030-drops-251101},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.29},
  annote =	{Keywords: Envy-Free Incomplete Connected Fair Division, Efficient Parameterized Approximation Scheme, W\lbrack1\rbrack-hardness}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.32
Fair Rent Division: New Budget and Rent Constraints

Authors: Rohith Reddy Gangam, Shayan Taherijam, and Vijay V. Vazirani

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the classical rent division problem, where n agents must allocate n indivisible rooms and split a fixed total rent R. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent’s room and rent to their own. This problem has been extensively studied under standard assumptions, where efficient algorithms for computing EF allocations are known. We extend this framework by introducing two practically motivated constraints: (i) lower and upper bounds on room rents, and (ii) room-specific budget for agents. We develop efficient combinatorial algorithms that either compute a feasible EF allocation or certify infeasibility. We further design algorithms to optimize over EF allocations using natural fairness objectives such as maximin utility, leximin utility, and minimum utility spread. Our approach unifies both constraint types within a single algorithmic framework, advancing the applicability of fair division methods in real-world platforms such as Spliddit.
Cite as

Rohith Reddy Gangam, Shayan Taherijam, and Vijay V. Vazirani. Fair Rent Division: New Budget and Rent Constraints. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gangam_et_al:LIPIcs.FSTTCS.2025.32,
  author =	{Gangam, Rohith Reddy and Taherijam, Shayan and Vazirani, Vijay V.},
  title =	{{Fair Rent Division: New Budget and Rent Constraints}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.32},
  URN =		{urn:nbn:de:0030-drops-251136},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.32},
  annote =	{Keywords: Rent Division, Envy‑Free, Fair Division}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.41
Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions

Authors: Yasushi Kawase, Bodhayan Roy, and Mohammad Azharuddin Sanpui

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
This paper explores the fair allocation of indivisible items in a multidimensional setting, motivated by the need to address fairness in complex environments where agents assess bundles according to multiple criteria. Such multidimensional settings are not merely of theoretical interest but are central to many real-world applications. For example, cloud computing resources are evaluated based on multiple criteria such as CPU cores, memory, and network bandwidth. In such cases, traditional one-dimensional fairness notions fail to capture fairness across multiple attributes. To address these challenges, we study two relaxed variants of envy-freeness: weak simultaneously envy-free up to c goods (weak sEFc) and strong simultaneously envy-free up to c goods (strong sEFc), which accommodate the multidimensionality of agents’ preferences. Under the weak notion, for every pair of agents and for each dimension, any perceived envy can be eliminated by removing, if necessary, a different set of goods from the envied agent’s allocation. In contrast, the strong version requires selecting a single set of goods whose removal from the envied bundle simultaneously eliminates envy in every dimension. We provide upper and lower bounds on the relaxation parameter c that guarantee the existence of weak or strong sEFc allocations, where these bounds are independent of the total number of items. In addition, we present algorithms for checking whether a weak or strong sEFc allocation exists. Moreover, we establish NP-hardness results for checking the existence of weak sEF1 and strong sEF1 allocations.
Cite as

Yasushi Kawase, Bodhayan Roy, and Mohammad Azharuddin Sanpui. Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kawase_et_al:LIPIcs.FSTTCS.2025.41,
  author =	{Kawase, Yasushi and Roy, Bodhayan and Sanpui, Mohammad Azharuddin},
  title =	{{Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.41},
  URN =		{urn:nbn:de:0030-drops-251210},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.41},
  annote =	{Keywords: Fair allocation, Envy-free up to one good, Multi-dimensional criteria, Linear programming, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.54
Reforming an Unfair Allocation by Exchanging Goods

Authors: Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1.
Cite as

Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong. Reforming an Unfair Allocation by Exchanging Goods. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{yuen_et_al:LIPIcs.ISAAC.2025.54,
  author =	{Yuen, Sheung Man and Igarashi, Ayumi and Kamiyama, Naoyuki and Suksompong, Warut},
  title =	{{Reforming an Unfair Allocation by Exchanging Goods}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{54:1--54:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.54},
  URN =		{urn:nbn:de:0030-drops-249626},
  doi =		{10.4230/LIPIcs.ISAAC.2025.54},
  annote =	{Keywords: fair division, indivisible goods, envy-freeness, exchanges}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.21
Pool Formation in Oceanic Games: Shapley Value and Proportional Sharing

Authors: Aggelos Kiayias, Elias Koutsoupias, Evangelos Markakis, and Panagiotis Tsamopoulos

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
We study a game-theoretic model for pool formation in Proof of Stake blockchain protocols. In such systems, stakeholders can form pools as a means of obtaining regular rewards from participation in ledger maintenance, with the power of each pool being dependent on its collective stake. The question we are interested in is the design of mechanisms, i.e., "reward sharing schemes," that suitably split rewards among pool members and achieve favorable properties in the resulting pool configuration. With this in mind, we initiate a non-cooperative game-theoretic analysis of the well known Shapley value scheme from cooperative game theory into the context of blockchains. In particular, we focus on the oceanic model of games, proposed by Milnor and Shapley (1978), which is suitable for populations where a small set of large players coexists with a big mass of rather small, negligible players. This provides an appropriate level of abstraction for pool formation processes that occur among the stakeholders of a blockchain. We provide comparisons between the Shapley mechanism and the more standard proportional scheme, in terms of attained decentralization, via a Price of Stability analysis and in terms of susceptibility to Sybil attacks, i.e., the strategic splitting of a players' stake with the intention of participating in multiple pools for increased profit. Interestingly, while the widely deployed proportional scheme appears to have certain advantages, the Shapley value scheme, which rewards higher the most pivotal players, emerges as a competitive alternative, by being able to bypass some of the downsides of proportional sharing in terms of Sybil attack susceptibility, while also not being far from optimal guarantees w.r.t. decentralization. Finally, we also complement our study with some variations of proportional sharing, where the profit is split in proportion to a superadditive or a subadditive function of the stake, showing that our results for the Shapley value scheme are maintained in comparison to these functions as well.
Cite as

Aggelos Kiayias, Elias Koutsoupias, Evangelos Markakis, and Panagiotis Tsamopoulos. Pool Formation in Oceanic Games: Shapley Value and Proportional Sharing. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kiayias_et_al:LIPIcs.AFT.2025.21,
  author =	{Kiayias, Aggelos and Koutsoupias, Elias and Markakis, Evangelos and Tsamopoulos, Panagiotis},
  title =	{{Pool Formation in Oceanic Games: Shapley Value and Proportional Sharing}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.21},
  URN =		{urn:nbn:de:0030-drops-247409},
  doi =		{10.4230/LIPIcs.AFT.2025.21},
  annote =	{Keywords: Shapley value, Nash equilibria, Price of Stability, Reward sharing schemes, Proof of Stake blockchains}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.98
The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization

Authors: Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the online allocation of divisible items to n agents with additive valuations for p-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti (2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of -∞ ≤ p ≤ 1. Surprisingly, our improved algorithms for all p ≤ (1)/(log n) are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.
Cite as

Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang. The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2025.98,
  author =	{Huang, Zhiyi and Lee, Chui Shan and Shu, Xinkai and Wang, Zhaozi},
  title =	{{The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{98:1--98:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.98},
  URN =		{urn:nbn:de:0030-drops-234754},
  doi =		{10.4230/LIPIcs.ICALP.2025.98},
  annote =	{Keywords: Online Algorithms, Fair Division, Nash Welfare}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.20
Group Fairness and Multi-Criteria Optimization in School Assignment

Authors: Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
We consider the problem of assigning students to schools when students have different utilities for schools and schools have limited capacities. The students belong to demographic groups, and fairness over these groups is captured either by concave objectives, or additional constraints on the utility of the groups. We present approximation algorithms for this assignment problem with group fairness via convex program rounding. These algorithms achieve various trade-offs between capacity violation and running time. We also show that our techniques easily extend to the setting where there are arbitrary constraints on the feasible assignment, capturing multi-criteria optimization. We present simulation results that demonstrate that the rounding methods are practical even on large problem instances, with the empirical capacity violation being much better than the theoretical bounds.
Cite as

Santhini K. A., Kamesh Munagala, Meghana Nasre, and Govind S. Sankar. Group Fairness and Multi-Criteria Optimization in School Assignment. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{k.a._et_al:LIPIcs.FORC.2025.20,
  author =	{K. A., Santhini and Munagala, Kamesh and Nasre, Meghana and S. Sankar, Govind},
  title =	{{Group Fairness and Multi-Criteria Optimization in School Assignment}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.20},
  URN =		{urn:nbn:de:0030-drops-231471},
  doi =		{10.4230/LIPIcs.FORC.2025.20},
  annote =	{Keywords: School Assignment, Approximation Algorithms, Group Fairness}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.41
Query Complexity of Stochastic Minimum Vertex Cover

Authors: Mahsa Derakhshan, Mohammad Saneian, and Zhiyang Xun

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

Abstract
We study the stochastic minimum vertex cover problem for general graphs. In this problem, we are given a graph G = (V, E) and an existence probability p_e for each edge e ∈ E. Edges of G are realized (or exist) independently with these probabilities, forming the realized subgraph 𝒢. The existence of an edge in 𝒢 can only be verified using edge queries. The goal of this problem is to find a near-optimal vertex cover of 𝒢 using a small number of queries. Previous work by Derakhshan, Durvasula, and Haghtalab [STOC 2023] established the existence of 1.5 + ε approximation algorithms for this problem with O(n/ε) queries. They also show that, under mild correlation among edge realizations, beating this approximation ratio requires querying a subgraph of size Ω(n ⋅ RS(n)). Here, RS(n) refers to Ruzsa-Szemerédi Graphs and represents the largest number of induced edge-disjoint matchings of size Θ(n) in an n-vertex graph. In this work, we design a simple algorithm for finding a (1 + ε) approximate vertex cover by querying a subgraph of size O(n ⋅ RS(n)) for any absolute constant ε > 0. Our algorithm can tolerate up to O(n ⋅ RS(n)) correlated edges, hence effectively completing our understanding of the problem under mild correlation.
Cite as

Mahsa Derakhshan, Mohammad Saneian, and Zhiyang Xun. Query Complexity of Stochastic Minimum Vertex Cover. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 41:1-41:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{derakhshan_et_al:LIPIcs.ITCS.2025.41,
  author =	{Derakhshan, Mahsa and Saneian, Mohammad and Xun, Zhiyang},
  title =	{{Query Complexity of Stochastic Minimum Vertex Cover}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{41:1--41:12},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-226691},
  doi =		{10.4230/LIPIcs.ITCS.2025.41},
  annote =	{Keywords: Sublinear algorithms, Vertex cover, Query complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.28
New Characterizations of Core Imputations of Matching and b-Matching Games

Authors: Vijay V. Vazirani

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
We give new characterizations of core imputations for the following games: 1) The assignment game. 2) Concurrent games, i.e., general graph matching games having non-empty core. 3) The unconstrained bipartite b-matching game (edges can be matched multiple times). 4) The constrained bipartite b-matching game (edges can be matched at most once). The classic paper of Shapley and Shubik [Shapley and Shubik, 1971] showed that core imputations of the assignment game are precisely optimal solutions to the dual of the LP-relaxation of the game. Building on this, Deng et al. [Deng et al., 1999] gave a general framework which yields analogous characterizations for several fundamental combinatorial games. Interestingly enough, their framework does not apply to the last two games stated above. In turn, we show that some of the core imputations of these games correspond to optimal dual solutions and others do not. This leads to the tantalizing question of understanding the origins of the latter. We also present new characterizations of the profits accrued by agents and teams in core imputations of the first two games. Our characterization for the first game is stronger than that for the second; the underlying reason is that the characterization of vertices of the Birkhoff polytope is stronger than that of the Balinski polytope.
Cite as

Vijay V. Vazirani. New Characterizations of Core Imputations of Matching and b-Matching Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 28:1-28:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{vazirani:LIPIcs.FSTTCS.2022.28,
  author =	{Vazirani, Vijay V.},
  title =	{{New Characterizations of Core Imputations of Matching and b-Matching Games}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.28},
  URN =		{urn:nbn:de:0030-drops-174207},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.28},
  annote =	{Keywords: LP-duality theory, cooperative game theory, core of a game, assignment game, general graph matching game, bipartite b-matching game}
}
Document
DOI: 10.4230/DagSemProc.07261.7
Efficient cost sharing with a cheap residual claimant

Authors: Hervé Moulin

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
For the cooperative production problem where the commons is a one dimensional convex cost function, I propose the residual mechanism to implement the efficient production level . In contrast to the familiar cost sharing methods such as serial, average and incremental, the residual mechanism may subsidize an agent with a null demand. IFor a large class of smooth cost functions, the residual mechanism generates a budget surplus that is, even in the worst case, vanishes as 1/logn where n is the number of participants. Compare with the serial, average and incremental mechanisms, of which the budget surplus, in the worst case, converges to the efficient surplus as n grows. The second problem is the assignment among n agents of p identical objects and cash transfers to compensate the losers. We assume p<n, and compute the optimal competitive performance among all VCG mechanisms generating no budget deficit. It goes to zero exponentially fast in n if the number of objects is fixed; and as (n)^(1/2) uniformly in p. The mechanism generates envy, and net utilities are not co-monotonic to valuations. When p>n/2, it may even fail to achieve voluntary participation.
Cite as

Hervé Moulin. Efficient cost sharing with a cheap residual claimant. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{moulin:DagSemProc.07261.7,
  author =	{Moulin, Herv\'{e}},
  title =	{{Efficient cost sharing with a cheap residual claimant}},
  booktitle =	{Fair Division},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.7},
  URN =		{urn:nbn:de:0030-drops-12312},
  doi =		{10.4230/DagSemProc.07261.7},
  annote =	{Keywords: Assignment, cost sharing, Vickrey-Clarke-Groves mechanisms, competitive analysis}
}
Document
DOI: 10.4230/DagSemProc.07271.16
Strategy-proof assignment with a vanishing budget surplus

Authors: Hervé Moulin

Published in: Dagstuhl Seminar Proceedings, Volume 7271, Computational Social Systems and the Internet (2007)

Abstract
A VCG mechanism to assign p identical objects is feasible is cash transfers yield no deficit. The efficiency loss of such a mechanism is the worst ratio of budget surplus to efficient surplus. We compute the optimal efficiency loss for all n and p, when we also require Voluntary Participation as well as when we do not. Without the VP requirement, the optimal efficiency loss converges to zero uniformly in p, and exponentially fast if p is fixed. With the VP requirement asymptotic budget balance is only true is p is not larger than n/2.
Cite as

Hervé Moulin. Strategy-proof assignment with a vanishing budget surplus. In Computational Social Systems and the Internet. Dagstuhl Seminar Proceedings, Volume 7271, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{moulin:DagSemProc.07271.16,
  author =	{Moulin, Herv\'{e}},
  title =	{{Strategy-proof assignment with a vanishing budget surplus}},
  booktitle =	{Computational Social Systems and the Internet},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7271},
  editor =	{Peter Cramton and Rudolf M\"{u}ller and Eva Tardos and Moshe Tennenholtz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07271.16},
  URN =		{urn:nbn:de:0030-drops-11608},
  doi =		{10.4230/DagSemProc.07271.16},
  annote =	{Keywords: VCG mechanisms, assignment, asymptotic budget balance, worst case analysis}
}
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