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Documents authored by Vinci, Cosimo

Document
DOI: 10.4230/LIPIcs.ESA.2024.26
Achieving Envy-Freeness Through Items Sale

Authors: Vittorio Bilò, Evangelos Markakis, and Cosimo Vinci

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider a fair division setting of allocating indivisible items to a set of agents. In order to cope with the well-known impossibility results related to the non-existence of envy-free allocations, we allow the option of selling some of the items so as to compensate envious agents with monetary rewards. In fact, this approach is not new in practice, as it is applied in some countries in inheritance or divorce cases. A drawback of this approach is that it may create a value loss, since the market value derived by selling an item can be less than the value perceived by the agents. Therefore, given the market values of all items, a natural goal is to identify which items to sell so as to arrive at an envy-free allocation, while at the same time maximizing the overall social welfare. Our work is focused on the algorithmic study of this problem, and we provide both positive and negative results on its approximability. When the agents have a commonly accepted value for each item, our results show a sharp separation between the cases of two or more agents. In particular, we establish a PTAS for two agents, and we complement this with a hardness result, that for three or more agents, the best approximation guarantee is provided by essentially selling all items. This hardness barrier, however, is relieved when the number of distinct item values is constant, as we provide an efficient algorithm for any number of agents. We also explore the generalization to heterogeneous valuations, where the hardness result continues to hold, and where we provide positive results for certain special cases.
Cite as

Vittorio Bilò, Evangelos Markakis, and Cosimo Vinci. Achieving Envy-Freeness Through Items Sale. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bilo_et_al:LIPIcs.ESA.2024.26,
  author =	{Bil\`{o}, Vittorio and Markakis, Evangelos and Vinci, Cosimo},
  title =	{{Achieving Envy-Freeness Through Items Sale}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{26:1--26:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.26},
  URN =		{urn:nbn:de:0030-drops-210977},
  doi =		{10.4230/LIPIcs.ESA.2024.26},
  annote =	{Keywords: Fair Item Allocation, Approximation Algorithms, Envy-freeness, Markets}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.59
Improved Approximation Factor for Adaptive Influence Maximization via Simple Greedy Strategies

Authors: Gianlorenzo D'Angelo, Debashmita Poddar, and Cosimo Vinci

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In the adaptive influence maximization problem, we are given a social network and a budget k, and we iteratively select k nodes, called seeds, in order to maximize the expected number of nodes that are reached by an influence cascade that they generate according to a stochastic model for influence diffusion. The decision on the next seed to select is based on the observed cascade of previously selected seeds. We focus on the myopic feedback model, in which we can only observe which neighbors of previously selected seeds have been influenced and on the independent cascade model, where each edge is associated with an independent probability of diffusing influence. While adaptive policies are strictly stronger than non-adaptive ones, in which all the seeds are selected beforehand, the latter are much easier to design and implement and they provide good approximation factors if the adaptivity gap, the ratio between the adaptive and the non-adaptive optima, is small. Previous works showed that the adaptivity gap is at most 4, and that simple adaptive or non-adaptive greedy algorithms guarantee an approximation of 1/4 (1-1/e) ≈ 0.158 for the adaptive optimum. This is the best approximation factor known so far for the adaptive influence maximization problem with myopic feedback. In this paper, we directly analyze the approximation factor of the non-adaptive greedy algorithm, without passing through the adaptivity gap, and show an improved bound of 1/2 (1-1/e) ≈ 0.316. Therefore, the adaptivity gap is at most 2e/e-1 ≈ 3.164. To prove these bounds, we introduce a new approach to relate the greedy non-adaptive algorithm to the adaptive optimum. The new approach does not rely on multi-linear extensions or random walks on optimal decision trees, which are commonly used techniques in the field. We believe that it is of independent interest and may be used to analyze other adaptive optimization problems. Finally, we also analyze the adaptive greedy algorithm, and show that guarantees an improved approximation factor of 1-1/(√{e)}≈ 0.393.
Cite as

Gianlorenzo D'Angelo, Debashmita Poddar, and Cosimo Vinci. Improved Approximation Factor for Adaptive Influence Maximization via Simple Greedy Strategies. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dangelo_et_al:LIPIcs.ICALP.2021.59,
  author =	{D'Angelo, Gianlorenzo and Poddar, Debashmita and Vinci, Cosimo},
  title =	{{Improved Approximation Factor for Adaptive Influence Maximization via Simple Greedy Strategies}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{59:1--59:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.59},
  URN =		{urn:nbn:de:0030-drops-141282},
  doi =		{10.4230/LIPIcs.ICALP.2021.59},
  annote =	{Keywords: Adaptive Optimization, Influence Maximization, Submodular Optimization, Stochastic Optimization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.14
Almost Envy-Free Allocations with Connected Bundles

Authors: Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, and William S. Zwicker

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph G. When the items are arranged in a path, we show that EF1 allocations are guaranteed to exist for arbitrary monotonic utility functions over bundles, provided that either there are at most four agents, or there are any number of agents but they all have identical utility functions. Our existence proofs are based on classical arguments from the divisible cake-cutting setting, and involve discrete analogues of cut-and-choose, of Stromquist's moving-knife protocol, and of the Su-Simmons argument based on Sperner's lemma. Sperner's lemma can also be used to show that on a path, an EF2 allocation exists for any number of agents. Except for the results using Sperner's lemma, all of our procedures can be implemented by efficient algorithms. Our positive results for paths imply the existence of connected EF1 or EF2 allocations whenever G is traceable, i.e., contains a Hamiltonian path. For the case of two agents, we completely characterize the class of graphs G that guarantee the existence of EF1 allocations as the class of graphs whose biconnected components are arranged in a path. This class is strictly larger than the class of traceable graphs; one can check in linear time whether a graph belongs to this class, and if so return an EF1 allocation.
Cite as

Vittorio Bilò, Ioannis Caragiannis, Michele Flammini, Ayumi Igarashi, Gianpiero Monaco, Dominik Peters, Cosimo Vinci, and William S. Zwicker. Almost Envy-Free Allocations with Connected Bundles. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bilo_et_al:LIPIcs.ITCS.2019.14,
  author =	{Bil\`{o}, Vittorio and Caragiannis, Ioannis and Flammini, Michele and Igarashi, Ayumi and Monaco, Gianpiero and Peters, Dominik and Vinci, Cosimo and Zwicker, William S.},
  title =	{{Almost Envy-Free Allocations with Connected Bundles}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.14},
  URN =		{urn:nbn:de:0030-drops-101078},
  doi =		{10.4230/LIPIcs.ITCS.2019.14},
  annote =	{Keywords: Envy-free Division, Cake-cutting, Resource Allocation, Algorithmic Game Theory}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.146
Uniform Mixed Equilibria in Network Congestion Games with Link Failures

Authors: Vittorio Bilò, Luca Moscardelli, and Cosimo Vinci

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
Motivated by possible applications in fault-tolerant routing, we introduce the notion of uniform mixed equilibria in network congestion games with adversarial link failures, where players need to route traffic from a source to a destination node. Given an integer rho >= 1, a rho-uniform mixed strategy is a mixed strategy in which a player plays exactly rho edge disjoint paths with uniform probabilities, so that a rho-uniform mixed equilibrium is a tuple of rho-uniform mixed strategies, one for each player, in which no player can lower her cost by deviating to another rho-uniform mixed strategy. For games with weighted players and affine latency functions, we show existence of rho-uniform mixed equilibria and provide a tight characterization of their price of anarchy. For games with unweighted players, instead, we extend the existential guarantee to any class of latency functions and, restricted to games with affine latencies, we derive a tight characterization of both the prices of anarchy and stability.
Cite as

Vittorio Bilò, Luca Moscardelli, and Cosimo Vinci. Uniform Mixed Equilibria in Network Congestion Games with Link Failures. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 146:1-146:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bilo_et_al:LIPIcs.ICALP.2018.146,
  author =	{Bil\`{o}, Vittorio and Moscardelli, Luca and Vinci, Cosimo},
  title =	{{Uniform Mixed Equilibria in Network Congestion Games with Link Failures}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{146:1--146:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.146},
  URN =		{urn:nbn:de:0030-drops-91508},
  doi =		{10.4230/LIPIcs.ICALP.2018.146},
  annote =	{Keywords: Network Congestion Games, Fault-Tolerant Routing, Nash Equilibria, Price of Anarchy, Price of Stability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.17
On the Impact of Singleton Strategies in Congestion Games

Authors: Vittorio Bilò and Cosimo Vinci

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
To what extent does the structure of the players' strategy space influence the efficiency of decentralized solutions in congestion games? In this work, we investigate whether better performance is possible when restricting to load balancing games in which players can only choose among single resources. We consider three different solutions concepts, namely, approximate pure Nash equilibria, approximate one-round walks generated by selfish players aiming at minimizing their personal cost and approximate one-round walks generated by cooperative players aiming at minimizing the marginal increase in the sum of the players' personal costs. The last two concepts can also be interpreted as solutions of simple greedy online algorithms for the related resource selection problem. Under fairly general latency functions on the resources, we show that, for all three types of solutions, better bounds cannot be achieved if players are either weighted or asymmetric. On the positive side, we prove that, under mild assumptions on the latency functions, improvements on the performance of approximate pure Nash equilibria are possible for load balancing games with weighted and symmetric players in the case of identical resources. We also design lower bounds on the performance of one-round walks in load balancing games with unweighted players and identical resources (in this case, solutions generated by selfish and cooperative players coincide).
Cite as

Vittorio Bilò and Cosimo Vinci. On the Impact of Singleton Strategies in Congestion Games. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bilo_et_al:LIPIcs.ESA.2017.17,
  author =	{Bil\`{o}, Vittorio and Vinci, Cosimo},
  title =	{{On the Impact of Singleton Strategies in Congestion Games}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.17},
  URN =		{urn:nbn:de:0030-drops-78576},
  doi =		{10.4230/LIPIcs.ESA.2017.17},
  annote =	{Keywords: Congestion games, Nash equilibrium, price of anarchy, online load balancing, greedy algorithms}
}
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