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Documents authored by Mahara, Ryoga

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.48
Reconfiguration of the Union of Arborescences

Authors: Yusuke Kobayashi, Ryoga Mahara, and Tamás Schwarcz

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
An arborescence in a digraph is an acyclic arc subset in which every vertex except a root has exactly one incoming arc. In this paper, we show the reconfigurability of the union of k arborescences for fixed k in the following sense: for any pair of arc subsets that can be partitioned into k arborescences, one can be transformed into the other by exchanging arcs one by one so that every intermediate arc subset can also be partitioned into k arborescences. This generalizes the result by Ito et al. (2023), who showed the case with k = 1. Since the union of k arborescences can be represented as a common matroid basis of two matroids, our result gives a new non-trivial example of matroid pairs for which two common bases are always reconfigurable to each other.
Cite as

Yusuke Kobayashi, Ryoga Mahara, and Tamás Schwarcz. Reconfiguration of the Union of Arborescences. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 48:1-48:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2023.48,
  author =	{Kobayashi, Yusuke and Mahara, Ryoga and Schwarcz, Tam\'{a}s},
  title =	{{Reconfiguration of the Union of Arborescences}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{48:1--48:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.48},
  URN =		{urn:nbn:de:0030-drops-193502},
  doi =		{10.4230/LIPIcs.ISAAC.2023.48},
  annote =	{Keywords: Arborescence packing, common matroid basis, combinatorial reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.55
Proportional Allocation of Indivisible Goods up to the Least Valued Good on Average

Authors: Yusuke Kobayashi and Ryoga Mahara

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study the problem of fairly allocating a set of indivisible goods to multiple agents and focus on the proportionality, which is one of the classical fairness notions. Since proportional allocations do not always exist when goods are indivisible, approximate notions of proportionality have been considered in the previous work. Among them, proportionality up to the maximin good (PROPm) has been the best approximate notion of proportionality that can be achieved for all instances. In this paper, we introduce the notion of proportionality up to the least valued good on average (PROPavg), which is a stronger notion than PROPm, and show that a PROPavg allocation always exists. Our results establish PROPavg as a notable non-trivial fairness notion that can be achieved for all instances. Our proof is constructive, and based on a new technique that generalizes the cut-and-choose protocol.
Cite as

Yusuke Kobayashi and Ryoga Mahara. Proportional Allocation of Indivisible Goods up to the Least Valued Good on Average. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 55:1-55:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kobayashi_et_al:LIPIcs.ISAAC.2022.55,
  author =	{Kobayashi, Yusuke and Mahara, Ryoga},
  title =	{{Proportional Allocation of Indivisible Goods up to the Least Valued Good on Average}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{55:1--55:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.55},
  URN =		{urn:nbn:de:0030-drops-173402},
  doi =		{10.4230/LIPIcs.ISAAC.2022.55},
  annote =	{Keywords: Discrete Fair Division, Indivisible Goods, Proportionality}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.66
Extension of Additive Valuations to General Valuations on the Existence of EFX

Authors: Ryoga Mahara

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Envy-freeness is one of the most widely studied notions in fair division. Since envy-free allocations do not always exist when items are indivisible, several relaxations have been considered. Among them, possibly the most compelling concept is envy-freeness up to any item (EFX). We study the existence of EFX allocations for general valuations. The existence of EFX allocations is a major open problem. For general valuations, it is known that an EFX allocation always exists (i) when n = 2 or (ii) when all agents have identical valuations, where n is the number of agents. it is also known that an EFX allocation always exists when one can leave at most n-1 items unallocated. We develop new techniques and extend some results of additive valuations to general valuations on the existence of EFX allocations. We show that an EFX allocation always exists (i) when all agents have one of two general valuations or (ii) when the number of items is at most n+3. We also show that an EFX allocation always exists when one can leave at most n-2 items unallocated. In addition to the positive results, we construct an instance with n = 3 in which an existing approach does not work as it is.
Cite as

Ryoga Mahara. Extension of Additive Valuations to General Valuations on the Existence of EFX. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 66:1-66:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{mahara:LIPIcs.ESA.2021.66,
  author =	{Mahara, Ryoga},
  title =	{{Extension of Additive Valuations to General Valuations on the Existence of EFX}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.66},
  URN =		{urn:nbn:de:0030-drops-146478},
  doi =		{10.4230/LIPIcs.ESA.2021.66},
  annote =	{Keywords: Discrete Fair Division, EFX allocations, General Valuations}
}
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