53 Search Results for "Barman, Siddharth"

Volume

LIPIcs, Volume 323

44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

FSTTCS 2024, December 16-18, 2024, Gandhinagar, Gujarat, India

Editors: Siddharth Barman and Sławomir Lasota

Document
DOI: 10.4230/LIPIcs.SWAT.2026.8
Submodular Max-Min Allocation Under Identical Valuations

Authors: Kimon Boehmer

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
In the problem of Submodular Max-Min Allocation, we are given a set of items, a set of players, and monotone submodular valuation functions that represent the satisfaction of a player with a certain subset of items. The goal is to find an allocation of the items to the players that maximizes the lowest satisfaction among all players. We study this problem in the special case where all players have the same valuation function. We devise a greedy algorithm which gives a 0.4-approximation, improving the previously best factor of 10/27 ≈ 0.37 by Uziahu and Feige. Furthermore, we study the integrality gap of the configuration LP when players have identical valuations. By constructing a variable assignment to the dual from a primal integral solution, we give the first constant upper bound on the integrality gap for submodular valuations. Generalizing the result to the case where players' allocations must be independent in k given matroids, we derive a 𝒪(k)-estimation algorithm for max-min allocation subject to k matroid constraints under identical valuations.
Cite as

Kimon Boehmer. Submodular Max-Min Allocation Under Identical Valuations. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{boehmer:LIPIcs.SWAT.2026.8,
  author =	{Boehmer, Kimon},
  title =	{{Submodular Max-Min Allocation Under Identical Valuations}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.8},
  URN =		{urn:nbn:de:0030-drops-260446},
  doi =		{10.4230/LIPIcs.SWAT.2026.8},
  annote =	{Keywords: Submodularity, Approximation algorithms, Allocation, Configuration LP}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.31
Parametric Disjunctive Timed Networks

Authors: Étienne André, Swen Jacobs, and Engel Lefaucheux

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We consider distributed systems with an arbitrary number of processes, modelled by timed automata that communicate through location guards: a process can take a guarded transition if at least one other process is in a given location. In this work, we introduce parametric disjunctive timed networks, where each timed automaton may contain timing parameters, i.e., unknown constants. We investigate two problems: deciding the emptiness of the set of parameter valuations for which 1) a given location is reachable for at least one process (local property), and 2) a global state is reachable where all processes are in a given location (global property). Our main positive result is that the first problem is decidable for networks of processes with a single clock and without invariants; this result holds for arbitrarily many timing parameters - a setting with few known decidability results. However, it becomes undecidable when invariants are allowed, or when considering global properties, even for systems with a single parameter. This highlights the significant expressive power of invariants in these networks. Additionally, we exhibit further decidable subclasses by restraining the syntax of guards and invariants.
Cite as

Étienne André, Swen Jacobs, and Engel Lefaucheux. Parametric Disjunctive Timed Networks. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 31:1-31:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{andre_et_al:LIPIcs.CSL.2026.31,
  author =	{Andr\'{e}, \'{E}tienne and Jacobs, Swen and Lefaucheux, Engel},
  title =	{{Parametric Disjunctive Timed Networks}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{31:1--31:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.31},
  URN =		{urn:nbn:de:0030-drops-254562},
  doi =		{10.4230/LIPIcs.CSL.2026.31},
  annote =	{Keywords: parametrised verification, parametric timed automata, verification of infinite-state systems}
}
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.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.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.CCC.2025.16
Direct Sums for Parity Decision Trees

Authors: Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Direct sum theorems state that the cost of solving k instances of a problem is at least Ω(k) times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.
Cite as

Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan. Direct Sums for Parity Decision Trees. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 16:1-16:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{besselman_et_al:LIPIcs.CCC.2025.16,
  author =	{Besselman, Tyler and G\"{o}\"{o}s, Mika and Guo, Siyao and Maystre, Gilbert and Yuan, Weiqiang},
  title =	{{Direct Sums for Parity Decision Trees}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{16:1--16:38},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.16},
  URN =		{urn:nbn:de:0030-drops-237105},
  doi =		{10.4230/LIPIcs.CCC.2025.16},
  annote =	{Keywords: direct sum, parity decision trees, query complexity}
}
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.FSTTCS.2024.25
Better Boosting of Communication Oracles, or Not

Authors: Nathaniel Harms and Artur Riazanov

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
Suppose we have a two-party communication protocol for f which allows the parties to make queries to an oracle computing g; for example, they may query an Equality oracle. To translate this protocol into a randomized protocol, we must replace the oracle with a randomized subroutine for solving g. If q queries are made, the standard technique requires that we boost the error of each subroutine down to O(1/q), leading to communication complexity which grows as q log q. For which oracles g can this naïve boosting technique be improved? We focus on the oracles which can be computed by constant-cost randomized protocols, and show that the naïve boosting strategy can be improved for the Equality oracle but not the 1-Hamming Distance oracle. Two surprising consequences are (1) a new example of a problem where the cost of computing k independent copies grows superlinear in k, drastically simplifying the only previous example due to Blais & Brody (CCC 2019); and (2) a new proof that Equality is not complete for the class of constant-cost randomized communication (Harms, Wild, & Zamaraev, STOC 2022; Hambardzumyan, Hatami, & Hatami, Israel Journal of Mathematics 2022).
Cite as

Nathaniel Harms and Artur Riazanov. Better Boosting of Communication Oracles, or Not. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harms_et_al:LIPIcs.FSTTCS.2024.25,
  author =	{Harms, Nathaniel and Riazanov, Artur},
  title =	{{Better Boosting of Communication Oracles, or Not}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.25},
  URN =		{urn:nbn:de:0030-drops-222143},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.25},
  annote =	{Keywords: oracles, error reduction, communication complexity}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSTTCS.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Siddharth Barman and Sławomir Lasota

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{barman_et_al:LIPIcs.FSTTCS.2024.0,
  author =	{Barman, Siddharth and Lasota, S{\l}awomir},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.0},
  URN =		{urn:nbn:de:0030-drops-225754},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSTTCS.2024
LIPIcs, Volume 323, FSTTCS 2024, Complete Volume

Authors: Siddharth Barman and Sławomir Lasota

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
LIPIcs, Volume 323, FSTTCS 2024, Complete Volume
Cite as

44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 1-670, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{barman_et_al:LIPIcs.FSTTCS.2024,
  title =	{{LIPIcs, Volume 323, FSTTCS 2024, Complete Volume}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{1--670},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024},
  URN =		{urn:nbn:de:0030-drops-225763},
  doi =		{10.4230/LIPIcs.FSTTCS.2024},
  annote =	{Keywords: LIPIcs, Volume 323, FSTTCS 2024, Complete Volume}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2024.1
An Introduction to the Theory of Linear Integer Arithmetic (Invited Paper)

Authors: Dmitry Chistikov

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
Presburger arithmetic, or linear integer arithmetic (LIA), is a logic that allows one to express linear constraints on integers: equalities, inequalities, and divisibility by nonzero n ∈ ℤ. More formally, it is the first-order theory of integers with addition and ordering. This paper offers a short introduction: what can be expressed in this logical theory, decision problems, and automated reasoning methods. We begin with an elementary introduction, explaining the language of linear arithmetic constraints by examples. We adopt a theoretical perspective, focusing on the decision problem: determining the truth value of a logical sentence. The following three views on Presburger arithmetic give us three effective methods for decision procedures: a view from geometry (using semi-linear sets), from automata theory (using finite automata and recognizable sets), and from symbolic computation (using quantifier elimination). The decision problem for existential formulas of Presburger arithmetic is essentially the feasibility problem of integer linear programming. By a fundamental result due to Borosh and Treybig [Proc. Am. Math. Soc. 55(2), 1976] and Papadimitriou [J. ACM 28(4), 1981], it belongs to the complexity class NP. Echoing the three views discussed above, we sketch three proofs of this result and discuss how these ideas have been used and developed in the recent research literature. This is a companion paper for a conference talk focused on the three views on Presburger arithmetic and their applications. The reader will require background knowledge at the level of undergraduate computer science curricula. The discussion of complexity aspects is more advanced.
Cite as

Dmitry Chistikov. An Introduction to the Theory of Linear Integer Arithmetic (Invited Paper). In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 1:1-1:36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chistikov:LIPIcs.FSTTCS.2024.1,
  author =	{Chistikov, Dmitry},
  title =	{{An Introduction to the Theory of Linear Integer Arithmetic}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{1:1--1:36},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.1},
  URN =		{urn:nbn:de:0030-drops-221909},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.1},
  annote =	{Keywords: Logical theories of arithmetic, decision procedures}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2024.2
Advances in Algorithmic Meta Theorems (Invited Paper)

Authors: Sebastian Siebertz and Alexandre Vigny

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic ℒ can be solved efficiently on every class C of structures satisfying certain conditions. The most prominent logics studied in the field are (counting) monadic second-order logic (C)MSO and first-order logic FO and its extensions. The complexity of CMSO model checking in general and of FO model checking on monotone graph classes is very well understood. In recent years there has been a rapid and exciting development of new algorithmic meta theorems. On the one hand there has been major progress for FO model checking on hereditary graph classes. This progress was driven by the development of a combinatorial structure theory for the logically defined monadically stable and monadically dependent graph classes, as well as by the advent of the new width measure twinwidth. On the other hand new algorithmic meta theorems for new logics with expressive power between FO and CMSO offer a new unifying view on methods like the irrelevant vertex technique and recursive understanding. In this paper we overview the recent advances in algorithmic meta theorems and provide rough sketches for the methods to prove them.
Cite as

Sebastian Siebertz and Alexandre Vigny. Advances in Algorithmic Meta Theorems (Invited Paper). In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 2:1-2:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{siebertz_et_al:LIPIcs.FSTTCS.2024.2,
  author =	{Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Advances in Algorithmic Meta Theorems}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{2:1--2:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.2},
  URN =		{urn:nbn:de:0030-drops-221912},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.2},
  annote =	{Keywords: Algorithmic meta theorems, monadic second-order logic, first-order logic, disjoint paths logic, algorithmic graph structure theory}
}
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