4 Search Results for "Mikkelsen, Jesper W."

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.34
Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice

Authors: Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Radio Networks (RN) is one of the fundamental models for network communication where nodes can broadcast messages locally but their simultaneous transmissions can interfere with each other at their shared neighbors. This work focuses on performing the very fundamental primitive of Local Broadcast, in spite of the interferences. We investigate to what extent local knowledge, called advice, relating to the 2-local domination number γ₂ may speed up Local Broadcast. Specifically for each node and some dominating set, knowledge about some neighboring dominating node and the local number among the neighbors of that dominating node. We show that such advice is sufficient to build an efficient oblivious transmission schedule. Along those lines, we present three algorithms trading the level of adaptiveness (from oblivious to adaptive) for bits of advice per node (from O(log (Δγ₂)) to 1). All our algorithms complete Local Broadcast in Õ(Δγ₂²) rounds, where Δ is the maximum degree of the network. On the side of lower bounds, we show that, for each quasi-adaptive deterministic Local Broadcast algorithm, there is some RN that requires Ω(min{(min{Δ,γ₂}/log n)²,n}) communication rounds, where n is the number of network nodes. In quasi-adaptive protocols nodes may stop executing once its computational task is completed. To the best of our knowledge, this is the first (nearly) quadratic Local Broadcast (same message for all neighbors) lower bound in the RN model. Our lower bound is stronger than previous works in multiple ways: i) it is nearly quadratically better than the best known general lower bound for this class of algorithms, ii) it applies to a wider class of algorithms than previous work for fully oblivious, iii) it achieves similar time lower bound than previous work proved for a much more demanding Local Broadcast where each node sends a possibly different message to each neighbor, and iv) it takes into account the local domination parameter γ₂.
Cite as

Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garncarek_et_al:LIPIcs.ISAAC.2025.34,
  author =	{Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R. and Kutten, Shay and Mosteiro, Miguel A.},
  title =	{{Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{34:1--34:20},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-249426},
  doi =		{10.4230/LIPIcs.ISAAC.2025.34},
  annote =	{Keywords: Radio Networks, Local Broadcast, Distributed Deterministic Algorithms, Lower Bounds, Graph algorithms, Advice, Labeling Schemes, Local Domination}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.12
Distributed Computation with Local Advice

Authors: Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Krzysztof Nowicki, Dennis Olivetti, Eva Rotenberg, and Jukka Suomela

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
Algorithms with advice have received ample attention in the distributed and online settings, and they have recently proven useful also in dynamic settings. In this work we study local computation with advice: the goal is to solve a graph problem Π with a distributed algorithm in T(Δ) communication rounds, for some function T that only depends on the maximum degree Δ of the graph, and the key question is how many bits of advice per node are needed. Some of our results regard Locally Checkable Labeling problems (LCLs), which is an important family of problems that includes various coloring and orientation problems on finite-degree graphs. These are constraint-satisfaction graph problems that can be defined with a finite set of valid input/output-labeled neighborhoods. Our main results are: 1) Any locally checkable labeling problem can be solved with only 1 bit of advice per node in graphs with sub-exponential growth (the number of nodes within radius r is sub-exponential in r; for example, grids are such graphs). Moreover, we can make the set of nodes that carry advice bits arbitrarily sparse. As a corollary, any locally checkable labeling problem admits a locally checkable proof with 1 bit per node in graphs with sub-exponential growth. 2) The assumption of sub-exponential growth is complemented by a conditional lower bound: assuming the Exponential-Time Hypothesis, there are locally checkable labeling problems that cannot be solved in general with any constant number of bits per node. 3) In any graph we can find an almost-balanced orientation (indegrees and outdegrees differ by at most one) with 1 bit of advice per node, and again we can make the advice arbitrarily sparse. As a corollary, we can also compress an arbitrary subset of edges so that a node of degree d stores only d/2 + 2 bits, and we can decompress it locally, in T(Δ) rounds. 4) In any graph of maximum degree Δ, we can find a Δ-coloring (if it exists) with 1 bit of advice per node, and again, we can make the advice arbitrarily sparse. 5) In any 3-colorable graph, we can find a 3-coloring with 1 bit of advice per node. As a corollary, in bounded-degree graphs there is a locally checkable proof that certifies 3-colorability with 1 bit of advice per node, while prior work shows that this is not possible with a proof labeling scheme (PLS), which is a more restricted setting where the verifier can only see up to distance 1. Our work shows that for many problems the key threshold is not whether we can achieve 1 bit of advice per node, but whether we can make the advice arbitrarily sparse. To formalize this idea, we develop a general framework of composable schemas that enables us to build algorithms for local computation with advice in a modular fashion: once we have (1) a schema for solving Π₁ and (2) a schema for solving Π₂ assuming an oracle for Π₁, we can also compose them and obtain (3) a schema that solves Π₂ without the oracle. It turns out that many natural problems admit composable schemas, all of them can be solved with only 1 bit of advice, and we can make the advice arbitrarily sparse.
Cite as

Alkida Balliu, Sebastian Brandt, Fabian Kuhn, Krzysztof Nowicki, Dennis Olivetti, Eva Rotenberg, and Jukka Suomela. Distributed Computation with Local Advice. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2025.12,
  author =	{Balliu, Alkida and Brandt, Sebastian and Kuhn, Fabian and Nowicki, Krzysztof and Olivetti, Dennis and Rotenberg, Eva and Suomela, Jukka},
  title =	{{Distributed Computation with Local Advice}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.12},
  URN =		{urn:nbn:de:0030-drops-248295},
  doi =		{10.4230/LIPIcs.DISC.2025.12},
  annote =	{Keywords: Distributed graph algorithms, LOCAL model, computation with advice, locally checkable labeling problems, proof labeling schemes, locally checkable proofs, graph coloring, exponential-time hypothesis}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.39
Randomization Can Be as Helpful as a Glimpse of the Future in Online Computation

Authors: Jesper W. Mikkelsen

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. Intuitively, our direct product theorems say that if b bits of advice are needed to ensure a cost of at most t for some problem, then r*b bits of advice are needed to ensure a total cost of at most r*t when solving r independent instances of the problem. Using our direct product theorems, we are able to translate decades of research on randomized online algorithms to the advice complexity model. Doing so improves significantly on the previous best advice complexity lower bounds for many online problems, or provides the first known lower bounds. For example, we show that - A paging algorithm needs Omega(n) bits of advice to achieve a competitive ratio better than H_k = Omega(log k), where k is the cache size. Previously, it was only known that Omega(n) bits of advice were necessary to achieve a constant competitive ratio smaller than 5/4. - Every O(n^{1-epsilon})-competitive vertex coloring algorithm must use Omega(n log n) bits of advice. Previously, it was only known that Omega(n log n) bits of advice were necessary to be optimal. For certain online problems, including the MTS, k-server, metric matching, paging, list update, and dynamic binary search tree problem, we prove that randomization and sublinear advice are equally powerful (if the underlying metric space or node set is finite). This means that several long-standing open questions regarding randomized online algorithms can be equivalently stated as questions regarding online algorithms with sublinear advice. For example, we show that there exists a deterministic O(log k)-competitive k-server algorithm with sublinear advice if and only if there exists a randomized O(log k)-competitive k-server algorithm without advice. Technically, our main direct product theorem is obtained by extending an information theoretical lower bound technique due to Emek, Fraigniaud, Korman, and Rosén [ICALP'09].
Cite as

Jesper W. Mikkelsen. Randomization Can Be as Helpful as a Glimpse of the Future in Online Computation. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{mikkelsen:LIPIcs.ICALP.2016.39,
  author =	{Mikkelsen, Jesper W.},
  title =	{{Randomization Can Be as Helpful as a Glimpse of the Future in Online Computation}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{39:1--39:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.39},
  URN =		{urn:nbn:de:0030-drops-63199},
  doi =		{10.4230/LIPIcs.ICALP.2016.39},
  annote =	{Keywords: online algorithms, advice complexity, information theory, randomization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.116
Advice Complexity for a Class of Online Problems

Authors: Joan Boyar, Lene M. Favrholdt, Christian Kudahl, and Jesper W. Mikkelsen

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. We determine the advice complexity of a number of hard online problems including independent set, vertex cover, dominating set and several others. These problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that \log\left(1+\frac{(c-1)^{c-1}}{c^{c}}\right)n=\Theta (n/c) bits of advice are necessary and sufficient (up to an additive term of O(\log n)) to achieve a competitive ratio of c. This is done by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and Böckenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems. Previous results of Halldórsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is \Theta (n/c). Our results improve on this by providing an exact formula for the higher-order term. Böckenhauer et al. (ISAAC 2009) gave a lower bound of \Omega (n/c) and an upper bound of O((n\log c)/c) on the advice complexity of online disjoint path allocation. We improve on the upper bound by a factor of $\log c$. For the remaining problems, no bounds on their advice complexity were previously known.
Cite as

Joan Boyar, Lene M. Favrholdt, Christian Kudahl, and Jesper W. Mikkelsen. Advice Complexity for a Class of Online Problems. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 116-129, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{boyar_et_al:LIPIcs.STACS.2015.116,
  author =	{Boyar, Joan and Favrholdt, Lene M. and Kudahl, Christian and Mikkelsen, Jesper W.},
  title =	{{Advice Complexity for a Class of Online Problems}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{116--129},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.116},
  URN =		{urn:nbn:de:0030-drops-49086},
  doi =		{10.4230/LIPIcs.STACS.2015.116},
  annote =	{Keywords: online algorithms, advice complexity, asymmetric string guessing, advice complexity class AOC, covering designs}
}
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