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Documents authored by Miller, Avery

Document
DOI: 10.4230/LIPIcs.FUN.2026.30
Replacing Cops with Zombies

Authors: Fengyi Liu and Avery Miller

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
In the Cops and Robbers game, two players take turns to move their pieces in a given graph, and the goal of the Cop player is to have any of their pieces capture the piece controlled by the Robber player. In the Zombies and Survivors variant, the Zombie player is trying to catch the piece controlled by the Survivor player, but the pursuers are more restricted: the zombie pieces must always move, and must do so toward the survivor along a shortest path. Essentially, the zombies move in a 'brainless' way, which severely limits the design of algorithmic strategies. In a practical setting where the pursuers are robots or drones, the zombie strategies can be carried out by simpler/cheaper devices. This motivates the question: when can cops be replaced by zombies? In contrast to previous work that highlights graph classes where cops are significantly more useful when trying to catch the evader, we examine some situations where the simpler restricted movements imposed on zombies can be sufficient.
Cite as

Fengyi Liu and Avery Miller. Replacing Cops with Zombies. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu_et_al:LIPIcs.FUN.2026.30,
  author =	{Liu, Fengyi and Miller, Avery},
  title =	{{Replacing Cops with Zombies}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{30:1--30:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.30},
  URN =		{urn:nbn:de:0030-drops-257492},
  doi =		{10.4230/LIPIcs.FUN.2026.30},
  annote =	{Keywords: Pursuit-Evasion Games, Grid Graphs, Cop Number, Zombie Number, Throttling Number}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.29
Fast Deterministic Rendezvous in Labeled Lines

Authors: Avery Miller and Andrzej Pelc

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
Two mobile agents, starting from different nodes of a network modeled as a graph, and woken up at possibly different times, have to meet at the same node. This problem is known as rendezvous. Agents move in synchronous rounds. In each round, an agent can either stay idle or move to an adjacent node. We consider deterministic rendezvous in the infinite line, i.e., the infinite graph with all nodes of degree 2. Each node has a distinct label which is a positive integer. An agent currently located at a node can see its label and both ports 0 and 1 at the node. The time of rendezvous is the number of rounds until meeting, counted from the starting round of the earlier agent. We consider three scenarios. In the first scenario, each agent knows its position in the line, i.e., each of them knows its initial distance from the smallest-labeled node, on which side of this node it is located, and the direction towards it. For this scenario, we design a rendezvous algorithm working in time O(D), where D is the initial distance between the agents. This complexity is clearly optimal. In the second scenario, each agent knows a priori only the label of its starting node and the initial distance D between them. In this scenario, we design a rendezvous algorithm working in time O(Dlog^*𝓁), where 𝓁 is the larger label of the starting nodes. We also prove a matching lower bound Ω(Dlog^*𝓁). Finally, in the most general scenario, where each agent knows a priori only the label of its starting node, we design a rendezvous algorithm working in time O(D²(log^*𝓁)³), which is thus at most cubic in the lower bound. All our results remain valid (with small changes) for arbitrary finite lines and for cycles. Our algorithms are drastically better than approaches that use graph exploration, which have running times that depend on the size or diameter of the graph. Our main methodological tool, and the main novelty of the paper, is a two way reduction: from fast colouring of the infinite labeled line using a constant number of colours in the LOCAL model to fast rendezvous in this line, and vice-versa. In one direction we use fast node colouring to quickly break symmetry between the identical agents. In the other direction, a lower bound on colouring time implies a lower bound on the time of breaking symmetry between the agents, and hence a lower bound on their meeting time.
Cite as

Avery Miller and Andrzej Pelc. Fast Deterministic Rendezvous in Labeled Lines. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{miller_et_al:LIPIcs.DISC.2023.29,
  author =	{Miller, Avery and Pelc, Andrzej},
  title =	{{Fast Deterministic Rendezvous in Labeled Lines}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.29},
  URN =		{urn:nbn:de:0030-drops-191550},
  doi =		{10.4230/LIPIcs.DISC.2023.29},
  annote =	{Keywords: rendezvous, deterministic algorithm, mobile agent, labeled line, graph colouring}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.OPODIS.2019
LIPIcs, Vol. 153, OPODIS 2019, Complete Volume

Authors: Pascal Felber, Roy Friedman, Seth Gilbert, and Avery Miller

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract
LIPIcs, Vol. 153, OPODIS 2019, Complete Volume
Cite as

23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 1-564, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{felber_et_al:LIPIcs.OPODIS.2019,
  title =	{{LIPIcs, Vol. 153, OPODIS 2019, Complete Volume}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{1--564},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019},
  URN =		{urn:nbn:de:0030-drops-119510},
  doi =		{10.4230/LIPIcs.OPODIS.2019},
  annote =	{Keywords: LIPIcs, Vol. 153, OPODIS 2019, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.OPODIS.2019.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Pascal Felber, Roy Friedman, Seth Gilbert, and Avery Miller

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

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

23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 0:i-0:xxii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{felber_et_al:LIPIcs.OPODIS.2019.0,
  author =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{0:i--0:xxii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.0},
  URN =		{urn:nbn:de:0030-drops-117869},
  doi =		{10.4230/LIPIcs.OPODIS.2019.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
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