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Documents authored by Das, Avinandan

Document
DOI: 10.4230/LIPIcs.SWAT.2026.15
One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming

Authors: Avinandan Das

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

Abstract
This paper investigates the semi-streaming complexity of k-partial coloring, a generalization of proper graph coloring. For k ≥ 1, a k-partial coloring requires that each vertex v in an n-node graph is assigned a color such that at least min{k, deg(v)} of its neighbors are assigned colors different from its own. This framework naturally extends classical coloring problems: specifically, k-partial (k+1)-coloring and k-partial k-coloring generalize (Δ+1)-proper coloring and Δ-proper coloring, respectively. Prior works of Assadi, Chen, and Khanna [SODA 2019] and Assadi, Kumar, and Mittal [TheoretiCS 2023] show that both (Δ+1)-proper coloring and Δ-proper coloring admit one-pass randomized semi-streaming algorithms. We explore whether these efficiency gains extend to their partial coloring generalizations and reveal a sharp computational threshold: while k-partial (k+1)-coloring admits a one-pass randomized semi-streaming algorithm, the k-partial k-coloring remains semi-streaming intractable, effectively demonstrating a "dichotomy of one color" in the streaming model.
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Avinandan Das. One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{das:LIPIcs.SWAT.2026.15,
  author =	{Das, Avinandan},
  title =	{{One Color Makes All the Difference in the Tractability of Partial Coloring in Semi-Streaming}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{15:1--15:16},
  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.2026.15},
  URN =		{urn:nbn:de:0030-drops-260515},
  doi =		{10.4230/LIPIcs.SWAT.2026.15},
  annote =	{Keywords: Graph Coloring, Semi-streaming algorithms, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.19
Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL

Authors: Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, and Ronja Stimpert

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The online-LOCAL and SLOCAL models are extensions of the LOCAL model where nodes are processed in a sequential but potentially adversarial order. So far, the only problem we know of where the global memory of the online-LOCAL model has an advantage over SLOCAL is 3-coloring bipartite graphs. Recently, Chang et al. [PODC 2024] showed that even in grids, 3-coloring requires Ω(log n) locality in deterministic online-LOCAL. This result was subsequently extended by Akbari et al. [STOC 2025] to also hold in randomized online-LOCAL. However, both proofs heavily rely on the assumption that the algorithm does not have access to the orientation of the underlying grid. In this paper, we show how to lift this requirement and obtain the same lower bound (against either model) even when the algorithm is explicitly given a globally consistent orientation of the grid.
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Thomas Boudier, Filippo Casagrande, Avinandan Das, Massimo Equi, Henrik Lievonen, Augusto Modanese, and Ronja Stimpert. Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boudier_et_al:LIPIcs.OPODIS.2025.19,
  author =	{Boudier, Thomas and Casagrande, Filippo and Das, Avinandan and Equi, Massimo and Lievonen, Henrik and Modanese, Augusto and Stimpert, Ronja},
  title =	{{Orientation Does Not Help with 3-Coloring a Grid in Online-LOCAL}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.19},
  URN =		{urn:nbn:de:0030-drops-251925},
  doi =		{10.4230/LIPIcs.OPODIS.2025.19},
  annote =	{Keywords: coloring, locally checkable labeling problems, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2023.30
Distributed Partial Coloring via Gradual Rounding

Authors: Avinandan Das, Pierre Fraigniaud, and Adi Rosén

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)

Abstract
For k ≥ 0, k-partial (k+1)-coloring asks to color the nodes of an n-node graph using a palette of k+1 colors such that every node v has at least min{k,deg(v)} neighbors colored with colors different from its own color. Hence, proper (Δ+1)-coloring is the special case of k-partial (k+1)-coloring when k = Δ. Ghaffari and Kuhn [FOCS 2021] recently proved that there exists a deterministic distributed algorithm that solves proper (Δ+1)-coloring of n-node graphs with maximum degree Δ in O(log n ⋅ log²Δ) rounds under the LOCAL model of distributed computing. This breakthrough result is achieved via an original iterated rounding approach. Using the same technique, Ghaffari and Kuhn also showed that there exists a deterministic algorithm that solves proper O(a)-coloring of n-node graphs with arboricity a in O(log n ⋅ log³a) rounds. It directly follows from this latter result that k-partial O(k)-coloring can be solved deterministically in O(log n ⋅ log³k) rounds. We develop an extension of the Ghaffari and Kuhn algorithm for proper (Δ+1)-coloring, and show that it solves k-partial (k+1)-coloring, thus generalizing their main result. Our algorithm runs in O(log n ⋅ log³k) rounds, like the algorithm that follows from Ghaffari and Kuhn’s algorithm for graphs with bounded arboricity, but uses only k+1 color, i.e., the smallest number c of colors such that every graph has a k-partial c-coloring. Like all the previously mentioned algorithms, our algorithm actually solves the general list-coloring version of the problem. Specifically, every node v receives as input an integer demand d(v) ≤ deg(v), and a list of at least d(v)+1 colors. Every node must then output a color from its list such that the resulting coloring satisfies that every node v has at least d(v) neighbors with colors different from its own. Our algorithm solves this problem in O(log n ⋅ log³k) rounds where k = max_v d(v). Moreover, in the specific case where all lists of colors given to the nodes as input share a common colors c^* known to all nodes, one can save one log k factor. In particular, for standard k-partial (k+1)-coloring, which corresponds to the case where all nodes are given the same list {1,… ,k+1}, one can modify our algorithm so that it runs in O(log n ⋅ log²k) rounds, and thus matches the complexity of Ghaffari and Kuhn’s algorithm for (Δ+1)-coloring for k = Δ.
Cite as

Avinandan Das, Pierre Fraigniaud, and Adi Rosén. Distributed Partial Coloring via Gradual Rounding. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 30:1-30:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{das_et_al:LIPIcs.OPODIS.2023.30,
  author =	{Das, Avinandan and Fraigniaud, Pierre and Ros\'{e}n, Adi},
  title =	{{Distributed Partial Coloring via Gradual Rounding}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{30:1--30:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.30},
  URN =		{urn:nbn:de:0030-drops-195205},
  doi =		{10.4230/LIPIcs.OPODIS.2023.30},
  annote =	{Keywords: Distributed graph coloring, partial coloring, weak coloring}
}
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