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DOI: 10.4230/LIPIcs.DISC.2024.49

Brief Announcement: Decreasing Verification Radius in Local Certification

Authors: Jan Matyáš Křišťan and Josef Erik Sedláček

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract

This paper deals with local certification, specifically locally checkable proofs: given a graph property, the task is to certify whether a graph satisfies the property. The verification of this certification needs to be done locally without the knowledge of the whole graph. We examine the trade-off between the visibility radius and the size of certificates. We describe a procedure that decreases the radius by encoding the neighbourhood of each vertex into its certificate. We also provide a corresponding lower bound on the required certificate size increase, showing that such an approach is close to optimal.

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Jan Matyáš Křišťan and Josef Erik Sedláček. Brief Announcement: Decreasing Verification Radius in Local Certification. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 49:1-49:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kristan_et_al:LIPIcs.DISC.2024.49,
  author =	{K\v{r}i\v{s}\v{t}an, Jan Maty\'{a}\v{s} and Sedl\'{a}\v{c}ek, Josef Erik},
  title =	{{Brief Announcement: Decreasing Verification Radius in Local Certification}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{49:1--49:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.49},
  URN =		{urn:nbn:de:0030-drops-212773},
  doi =		{10.4230/LIPIcs.DISC.2024.49},
  annote =	{Keywords: Local certification, locally checkable proofs, proof-labeling schemes, graphs, distributed computing}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2024.54

Romeo and Juliet Is EXPTIME-Complete

Authors: Harmender Gahlawat, Jan Matyáš Křišťan, and Tomáš Valla

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract

Romeo and Juliet is a two player Rendezvous game played on graphs where one player controls two agents, Romeo (ℛ) and Juliet (𝒥) who aim to meet at a vertex against k adversaries, called dividers, controlled by the other player. The optimization in this game lies at deciding the minimum number of dividers sufficient to restrict ℛ and 𝒥 from meeting in a graph, called the dynamic separation number. We establish that Romeo and Juliet is EXPTIME-complete, settling a conjecture of Fomin, Golovach, and Thilikos [Inf. and Comp., 2023] positively. We also consider the game for directed graphs and establish that although the game is EXPTIME-complete for general directed graphs, it is PSPACE-complete and co-W[2]-hard for directed acyclic graphs.

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Harmender Gahlawat, Jan Matyáš Křišťan, and Tomáš Valla. Romeo and Juliet Is EXPTIME-Complete. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gahlawat_et_al:LIPIcs.MFCS.2024.54,
  author =	{Gahlawat, Harmender and K\v{r}i\v{s}\v{t}an, Jan Maty\'{a}\v{s} and Valla, Tom\'{a}\v{s}},
  title =	{{Romeo and Juliet Is EXPTIME-Complete}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.54},
  URN =		{urn:nbn:de:0030-drops-206106},
  doi =		{10.4230/LIPIcs.MFCS.2024.54},
  annote =	{Keywords: Rendezvous Games on graphs, EXPTIME-completeness, Dynamic Separators}
}

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Documents authored by Křišťan, Jan Matyáš

Brief Announcement: Decreasing Verification Radius in Local Certification

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Romeo and Juliet Is EXPTIME-Complete

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