DROPS

Document

DOI: 10.4230/LIPIcs.STACS.2024.15

An Improved Approximation Algorithm for Dynamic Minimum Linear Arrangement

Authors: Marcin Bienkowski and Guy Even

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract

The dynamic offline linear arrangement problem deals with reordering n elements subject to a sequence of edge requests. The input consists of a sequence of m edges (i.e., unordered pairs of elements). The output is a sequence of permutations (i.e., bijective mapping of the elements to n equidistant points). In step t, the order of the elements is changed to the t-th permutation, and then the t-th request is served. The cost of the output consists of two parts per step: request cost and rearrangement cost. The former is the current distance between the endpoints of the request, while the latter is proportional to the number of adjacent element swaps required to move from one permutation to the consecutive permutation. The goal is to find a minimum cost solution. We present a deterministic O(log n log log n)-approximation algorithm for this problem, improving over a randomized O(log² n)-approximation by Olver et al. [Neil Olver et al., 2018]. Our algorithm is based on first solving spreading-metric LP relaxation on a time-expanded graph, applying a tree decomposition on the basis of the LP solution, and finally converting the tree decomposition to a sequence of permutations. The techniques we employ are general and have the potential to be useful for other dynamic graph optimization problems.

Cite as

Marcin Bienkowski and Guy Even. An Improved Approximation Algorithm for Dynamic Minimum Linear Arrangement. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bienkowski_et_al:LIPIcs.STACS.2024.15,
  author =	{Bienkowski, Marcin and Even, Guy},
  title =	{{An Improved Approximation Algorithm for Dynamic Minimum Linear Arrangement}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.15},
  URN =		{urn:nbn:de:0030-drops-197252},
  doi =		{10.4230/LIPIcs.STACS.2024.15},
  annote =	{Keywords: Minimum Linear Arrangement, dynamic Variant, Optimization Problems, Graph Problems, approximation Algorithms}
}

Document

DOI: 10.4230/DagRep.13.6.1

Scalable Analysis of Probabilistic Models and Programs (Dagstuhl Seminar 23241)

Authors: Sebastian Junges, Joost-Pieter Katoen, Scott Sanner, Guy Van den Broeck, and Bahare Salmani

Published in: Dagstuhl Reports, Volume 13, Issue 6 (2024)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 23241 "Scalable Analysis of Probabilistic Models and Programs". The seminar brought together researchers from probabilistic graphical models, verification of probabilistic programming languages, and probabilistic planning. The communities bring vastly different perspectives on the methods and goals of inference under uncertainty. In this seminar, we worked towards a common understanding of how the different angles yield subtle differences in the problem statements and how the different methods provide different strengths and weaknesses. The report describes the different areas, the activities during the seminar including hot topics that were vividly discussed, and an overview of the technical talks.

Cite as

Sebastian Junges, Joost-Pieter Katoen, Scott Sanner, Guy Van den Broeck, and Bahare Salmani. Scalable Analysis of Probabilistic Models and Programs (Dagstuhl Seminar 23241). In Dagstuhl Reports, Volume 13, Issue 6, pp. 1-21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{junges_et_al:DagRep.13.6.1,
  author =	{Junges, Sebastian and Katoen, Joost-Pieter and Sanner, Scott and Van den Broeck, Guy and Salmani, Bahare},
  title =	{{Scalable Analysis of Probabilistic Models and Programs (Dagstuhl Seminar 23241)}},
  pages =	{1--21},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{6},
  editor =	{Junges, Sebastian and Katoen, Joost-Pieter and Sanner, Scott and Van den Broeck, Guy and Salmani, Bahare},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.13.6.1},
  URN =		{urn:nbn:de:0030-drops-196362},
  doi =		{10.4230/DagRep.13.6.1},
  annote =	{Keywords: model counting, probabilistic inference, probabilistic model checking, probabilistic planning, probabilistic programs}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2024.34

On Parallel Repetition of PCPs

Authors: Alessandro Chiesa, Ziyi Guan, and Burcu Yıldız

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

Parallel repetition refers to a set of valuable techniques used to reduce soundness error of probabilistic proofs while saving on certain efficiency measures. Parallel repetition has been studied for interactive proofs (IPs) and multi-prover interactive proofs (MIPs). In this paper we initiate the study of parallel repetition for probabilistically checkable proofs (PCPs). We show that, perhaps surprisingly, parallel repetition of a PCP can increase soundness error, in fact bringing the soundness error to one as the number of repetitions tends to infinity. This "failure" of parallel repetition is common: we find that it occurs for a wide class of natural PCPs for NP-complete languages. We explain this unexpected phenomenon by providing a characterization result: the parallel repetition of a PCP brings the soundness error to zero if and only if a certain "MIP projection" of the PCP has soundness error strictly less than one. We show that our characterization is tight via a suitable example. Moreover, for those cases where parallel repetition of a PCP does bring the soundness error to zero, the aforementioned connection to MIPs offers preliminary results on the rate of decay of the soundness error. Finally, we propose a simple variant of parallel repetition, called consistent parallel repetition (CPR), which has the same randomness complexity and query complexity as the plain variant of parallel repetition. We show that CPR brings the soundness error to zero for every PCP (with non-trivial soundness error). In fact, we show that CPR decreases the soundness error at an exponential rate in the repetition parameter.

Cite as

Alessandro Chiesa, Ziyi Guan, and Burcu Yıldız. On Parallel Repetition of PCPs. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chiesa_et_al:LIPIcs.ITCS.2024.34,
  author =	{Chiesa, Alessandro and Guan, Ziyi and Y{\i}ld{\i}z, Burcu},
  title =	{{On Parallel Repetition of PCPs}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{34:1--34:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.34},
  URN =		{urn:nbn:de:0030-drops-195629},
  doi =		{10.4230/LIPIcs.ITCS.2024.34},
  annote =	{Keywords: probabilistically checkable proofs, parallel repetition}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2023.22

Collective Graph Exploration Parameterized by Vertex Cover

Authors: Siddharth Gupta, Guy Sa'ar, and Meirav Zehavi

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract

We initiate the study of the parameterized complexity of the Collective Graph Exploration (CGE) problem. In CGE, the input consists of an undirected connected graph G and a collection of k robots, initially placed at the same vertex r of G, and each one of them has an energy budget of B. The objective is to decide whether G can be explored by the k robots in B time steps, i.e., there exist k closed walks in G, one corresponding to each robot, such that every edge is covered by at least one walk, every walk starts and ends at the vertex r, and the maximum length of any walk is at most B. Unfortunately, this problem is NP-hard even on trees [Fraigniaud et al., 2006]. Further, we prove that the problem remains W[1]-hard parameterized by k even for trees of treedepth 3. Due to the para-NP-hardness of the problem parameterized by treedepth, and motivated by real-world scenarios, we study the parameterized complexity of the problem parameterized by the vertex cover number (vc) of the graph, and prove that the problem is fixed-parameter tractable (FPT) parameterized by vc. Additionally, we study the optimization version of CGE, where we want to optimize B, and design an approximation algorithm with an additive approximation factor of O(vc).

Cite as

Siddharth Gupta, Guy Sa'ar, and Meirav Zehavi. Collective Graph Exploration Parameterized by Vertex Cover. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gupta_et_al:LIPIcs.IPEC.2023.22,
  author =	{Gupta, Siddharth and Sa'ar, Guy and Zehavi, Meirav},
  title =	{{Collective Graph Exploration Parameterized by Vertex Cover}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.22},
  URN =		{urn:nbn:de:0030-drops-194413},
  doi =		{10.4230/LIPIcs.IPEC.2023.22},
  annote =	{Keywords: Collective Graph Exploration, Parameterized Complexity, Approximation Algorithm, Vertex Cover, Treedepth}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2023.23

Drawn Tree Decomposition: New Approach for Graph Drawing Problems

Authors: Siddharth Gupta, Guy Sa'ar, and Meirav Zehavi

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such algorithms. An even more serious issue is that, here, "standard" parameters very often yield intractability. In particular, for the most common structural parameter, namely, treewidth, we frequently observe NP-hardness already when the input graphs are restricted to have constant (often, being just 1 or 2) treewidth. Our work deals with both drawbacks simultaneously. We introduce a novel form of tree decomposition that, roughly speaking, does not decompose (only) a graph, but an entire drawing. As such, its bags and separators are of geometric (rather than only combinatorial) nature. While the corresponding parameter - like treewidth - can be arbitrarily smaller than the height (and width) of the drawing, we show that - unlike treewidth - it gives rise to efficient algorithms. Specifically, we get slice-wise polynomial (XP) time algorithms parameterized by our parameter. We present a general scheme for the design of such algorithms, and apply it to several central problems in Graph Drawing, including the recognition of grid graphs, minimization of crossings and bends, and compaction. Other than for the class of problems we discussed in the paper, we believe that our decomposition and scheme are of independent interest and can be further extended or generalized to suit even a wider class of problems. Additionally, we discuss classes of drawings where our parameter is bounded by 𝒪(√n) (where n is the number of vertices of the graph), yielding subexponential-time algorithms. Lastly, we prove which relations exist between drawn treewidth and other width measures, including treewidth, pathwidth, (dual) carving-width and embedded-width.

Cite as

Siddharth Gupta, Guy Sa'ar, and Meirav Zehavi. Drawn Tree Decomposition: New Approach for Graph Drawing Problems. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gupta_et_al:LIPIcs.IPEC.2023.23,
  author =	{Gupta, Siddharth and Sa'ar, Guy and Zehavi, Meirav},
  title =	{{Drawn Tree Decomposition: New Approach for Graph Drawing Problems}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.23},
  URN =		{urn:nbn:de:0030-drops-194424},
  doi =		{10.4230/LIPIcs.IPEC.2023.23},
  annote =	{Keywords: Graph Drawing, Parameterized Complexity, Tree decomposition}
}

Document

DOI: 10.4230/LIPIcs.AFT.2023.5

Security Analysis of Filecoin’s Expected Consensus in the Byzantine vs Honest Model

Authors: Xuechao Wang, Sarah Azouvi, and Marko Vukolić

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)

Abstract

Filecoin is the largest storage-based open-source blockchain, both by storage capacity (>11EiB) and market capitalization. This paper provides the first formal security analysis of Filecoin’s consensus (ordering) protocol, Expected Consensus (EC). Specifically, we show that EC is secure against an arbitrary adversary that controls a fraction β of the total storage for β m < 1- e^{-(1-β)m}, where m is a parameter that corresponds to the expected number of blocks per round, currently m = 5 in Filecoin. We then present an attack, the n-split attack, where an adversary splits the honest miners between multiple chains, and show that it is successful for β m ≥ 1- e^{-(1-β)m}, thus proving that β m = 1- e^{-(1-β)m} is the tight security threshold of EC. This corresponds roughly to an adversary with 20% of the total storage pledged to the chain. Finally, we propose two improvements to EC security that would increase this threshold. One of these two fixes is being implemented as a Filecoin Improvement Proposal (FIP).

Cite as

Xuechao Wang, Sarah Azouvi, and Marko Vukolić. Security Analysis of Filecoin’s Expected Consensus in the Byzantine vs Honest Model. In 5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wang_et_al:LIPIcs.AFT.2023.5,
  author =	{Wang, Xuechao and Azouvi, Sarah and Vukoli\'{c}, Marko},
  title =	{{Security Analysis of Filecoin’s Expected Consensus in the Byzantine vs Honest Model}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023.5},
  URN =		{urn:nbn:de:0030-drops-191943},
  doi =		{10.4230/LIPIcs.AFT.2023.5},
  annote =	{Keywords: Decentralized storage, Consensus, Security analysis}
}

Document

DOI: 10.4230/LIPIcs.DISC.2023.6

Base Fee Manipulation in Ethereum’s EIP-1559 Transaction Fee Mechanism

Authors: Sarah Azouvi, Guy Goren, Lioba Heimbach, and Alexander Hicks

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

Abstract

In 2021 Ethereum adjusted the transaction pricing mechanism by implementing EIP-1559, which introduces the base fee - a network fee that is burned and dynamically adjusts to the network demand. The authors of the Ethereum Improvement Proposal (EIP) noted that a miner with more than 50% of the mining power could be incentivized to deviate from the honest mining strategy. Instead, such a miner could propose a series of empty blocks to artificially lower demand and increase her future rewards. In this paper, we generalize this attack and show that under rational player behavior, deviating from the honest strategy can be profitable for a miner with less than 50% of the mining power. We show that even when miners do not collaborate, it is at times rational for smaller miners to join the attack. Finally, we propose a mitigation to address the identified vulnerability.

Cite as

Sarah Azouvi, Guy Goren, Lioba Heimbach, and Alexander Hicks. Base Fee Manipulation in Ethereum’s EIP-1559 Transaction Fee Mechanism. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{azouvi_et_al:LIPIcs.DISC.2023.6,
  author =	{Azouvi, Sarah and Goren, Guy and Heimbach, Lioba and Hicks, Alexander},
  title =	{{Base Fee Manipulation in Ethereum’s EIP-1559 Transaction Fee Mechanism}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{6:1--6:22},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.6},
  URN =		{urn:nbn:de:0030-drops-191325},
  doi =		{10.4230/LIPIcs.DISC.2023.6},
  annote =	{Keywords: blockchain, Ethereum, transaction fee mechanism, EIP-1559}
}

Document

DOI: 10.4230/LIPIcs.DISC.2023.8

Treasure Hunt with Volatile Pheromones

Authors: Evangelos Bampas, Joffroy Beauquier, Janna Burman, and William Guy--Obé

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

Abstract

In the treasure hunt problem, a team of mobile agents need to locate a single treasure that is hidden in their environment. We consider the problem in the discrete setting of an oriented infinite rectangular grid, where agents are modeled as synchronous identical deterministic time-limited finite-state automata, originating at a rate of one agent per round from the origin. Agents perish τ rounds after their creation, where τ ≥ 1 is a parameter of the model. An algorithm solves the treasure hunt problem if every grid position at distance τ or less from the origin is visited by at least one agent. Agents may communicate only by leaving indistinguishable traces (pheromone) on the nodes of the grid, which can be sensed by agents in adjacent nodes and thus modify their behavior. The novelty of our approach is that, in contrast to existing literature that uses permanent pheromone markers, we assume that pheromone traces evaporate over μ rounds from the moment they were placed on a node, where μ ≥ 1 is another parameter of the model. We look for uniform algorithms that solve the problem without knowledge of the parameter values, and we investigate the implications of this very weak communication mechanism to the treasure hunt problem. We show that, if pheromone persists for at least two rounds (μ ≥ 2), then there exists a treasure hunt algorithm for all values of agent lifetime. We also develop a more sophisticated algorithm that works for all values of μ, hence also for the fastest possible pheromone evaporation of μ = 1, but only if agent lifetime is at least 16.

Cite as

Evangelos Bampas, Joffroy Beauquier, Janna Burman, and William Guy--Obé. Treasure Hunt with Volatile Pheromones. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bampas_et_al:LIPIcs.DISC.2023.8,
  author =	{Bampas, Evangelos and Beauquier, Joffroy and Burman, Janna and Guy--Ob\'{e}, William},
  title =	{{Treasure Hunt with Volatile Pheromones}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{8:1--8:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.8},
  URN =		{urn:nbn:de:0030-drops-191343},
  doi =		{10.4230/LIPIcs.DISC.2023.8},
  annote =	{Keywords: Mobile Agents, Exploration, Search, Treasure Hunt, Pheromone, Evaporation}
}

Document

DOI: 10.4230/LIPIcs.DISC.2023.30

Null Messages, Information and Coordination

Authors: Raïssa Nataf, Guy Goren, and Yoram Moses

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

Abstract

This paper investigates the role that null messages play in synchronous systems with and without failures, and provides necessary and sufficient conditions on the structure of protocols for information transfer and coordination there. We start by introducing a new and more refined definition of null messages. A generalization of message chains that allow these null messages is provided, and is shown to be necessary and sufficient for information transfer in reliable systems. Coping with crash failures requires a much richer structure, since not receiving a message may be the result of the sender’s failure. We introduce a class of communication patterns called resilient message blocks, which impose a stricter condition on protocols than the silent choirs of Goren and Moses (2020). Such blocks are shown to be necessary for information transfer in crash-prone systems. Moreover, they are sufficient in several cases of interest, in which silent choirs are not. Finally, a particular combination of resilient message blocks is shown to be necessary and sufficient for solving the Ordered Response coordination problem.

Cite as

Raïssa Nataf, Guy Goren, and Yoram Moses. Null Messages, Information and Coordination. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{nataf_et_al:LIPIcs.DISC.2023.30,
  author =	{Nataf, Ra\"{i}ssa and Goren, Guy and Moses, Yoram},
  title =	{{Null Messages, Information and Coordination}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{30:1--30:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.30},
  URN =		{urn:nbn:de:0030-drops-191564},
  doi =		{10.4230/LIPIcs.DISC.2023.30},
  annote =	{Keywords: null messages, fault tolerance, coordination, information flow, knowledge analysis}
}

Document

DOI: 10.4230/LIPIcs.CP.2023.19

An Efficient Constraint Programming Approach to Preemptive Job Shop Scheduling

Authors: Carla Juvin, Emmanuel Hebrard, Laurent Houssin, and Pierre Lopez

Published in: LIPIcs, Volume 280, 29th International Conference on Principles and Practice of Constraint Programming (CP 2023)

Abstract

Constraint Programming has been widely, and very successfully, applied to scheduling problems. However, the focus has been on uninterruptible tasks, and preemptive scheduling problems are typically harder for existing constraint solvers. Indeed, one usually needs to represent all potential task interruptions thus introducing many variables and symmetrical or dominated choices. In this paper, building on mostly known results, we observe that a large class of preemptive disjunctive scheduling problems do not require an explicit model of task interruptions. We then introduce a new constraint programming approach for this class of problems that significantly outperforms state-of-the-art dedicated approaches in our experimental results.

Cite as

Carla Juvin, Emmanuel Hebrard, Laurent Houssin, and Pierre Lopez. An Efficient Constraint Programming Approach to Preemptive Job Shop Scheduling. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{juvin_et_al:LIPIcs.CP.2023.19,
  author =	{Juvin, Carla and Hebrard, Emmanuel and Houssin, Laurent and Lopez, Pierre},
  title =	{{An Efficient Constraint Programming Approach to Preemptive Job Shop Scheduling}},
  booktitle =	{29th International Conference on Principles and Practice of Constraint Programming (CP 2023)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-300-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{280},
  editor =	{Yap, Roland H. C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2023.19},
  URN =		{urn:nbn:de:0030-drops-190568},
  doi =		{10.4230/LIPIcs.CP.2023.19},
  annote =	{Keywords: Constraint Programming, Scheduling, Preemptive Resources}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2023.16

A Game of Pawns

Authors: Guy Avni, Pranav Ghorpade, and Shibashis Guha

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its next location. This leads to a path in the graph, which determines the winner. Traditionally, the control of vertices is predetermined and fixed. The novelty of pawn games is that control of vertices changes dynamically throughout the game as follows. Each vertex of a pawn game is owned by a pawn. In each turn, the pawns are partitioned between the two players, and the player who controls the pawn that owns the vertex on which the token is located, chooses the next location of the token. Control of pawns changes dynamically throughout the game according to a fixed mechanism. Specifically, we define several grabbing-based mechanisms in which control of at most one pawn transfers at the end of each turn. We study the complexity of solving pawn games, where we focus on reachability objectives and parameterize the problem by the mechanism that is being used and by restrictions on pawn ownership of vertices. On the positive side, even though pawn games are exponentially-succinct turn-based games, we identify several natural classes that can be solved in PTIME. On the negative side, we identify several EXPTIME-complete classes, where our hardness proofs are based on a new class of games called Lock & Key games, which may be of independent interest.

Cite as

Guy Avni, Pranav Ghorpade, and Shibashis Guha. A Game of Pawns. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{avni_et_al:LIPIcs.CONCUR.2023.16,
  author =	{Avni, Guy and Ghorpade, Pranav and Guha, Shibashis},
  title =	{{A Game of Pawns}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.16},
  URN =		{urn:nbn:de:0030-drops-190100},
  doi =		{10.4230/LIPIcs.CONCUR.2023.16},
  annote =	{Keywords: Graph games, Reachability games, Pawn games, Dynamic vertex control}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2023.26

DNN Verification, Reachability, and the Exponential Function Problem

Authors: Omri Isac, Yoni Zohar, Clark Barrett, and Guy Katz

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract

Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges, the verification community has begun developing techniques for rigorously analyzing DNNs, with numerous verification algorithms proposed in recent years. While a significant amount of work has gone into developing these verification algorithms, little work has been devoted to rigorously studying the computability and complexity of the underlying theoretical problems. Here, we seek to contribute to the bridging of this gap. We focus on two kinds of DNNs: those that employ piecewise-linear activation functions (e.g., ReLU), and those that employ piecewise-smooth activation functions (e.g., Sigmoids). We prove the two following theorems: (i) the decidability of verifying DNNs with a particular set of piecewise-smooth activation functions, including Sigmoid and tanh, is equivalent to a well-known, open problem formulated by Tarski; and (ii) the DNN verification problem for any quantifier-free linear arithmetic specification can be reduced to the DNN reachability problem, whose approximation is NP-complete. These results answer two fundamental questions about the computability and complexity of DNN verification, and the ways it is affected by the network’s activation functions and error tolerance; and could help guide future efforts in developing DNN verification tools.

Cite as

Omri Isac, Yoni Zohar, Clark Barrett, and Guy Katz. DNN Verification, Reachability, and the Exponential Function Problem. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{isac_et_al:LIPIcs.CONCUR.2023.26,
  author =	{Isac, Omri and Zohar, Yoni and Barrett, Clark and Katz, Guy},
  title =	{{DNN Verification, Reachability, and the Exponential Function Problem}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.26},
  URN =		{urn:nbn:de:0030-drops-190205},
  doi =		{10.4230/LIPIcs.CONCUR.2023.26},
  annote =	{Keywords: Formal Verification, Computability Theory, Deep Neural Networks}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.26

The Geometry of Tree-Based Sorting

Authors: Guy E. Blelloch and Magdalen Dobson

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

We study the connections between sorting and the binary search tree (BST) model, with an aim towards showing that the fields are connected more deeply than is currently appreciated. While any BST can be used to sort by inserting the keys one-by-one, this is a very limited relationship and importantly says nothing about parallel sorting. We show what we believe to be the first formal relationship between the BST model and sorting. Namely, we show that a large class of sorting algorithms, which includes mergesort, quicksort, insertion sort, and almost every instance-optimal sorting algorithm, are equivalent in cost to offline BST algorithms. Our main theoretical tool is the geometric interpretation of the BST model introduced by Demaine et al. [Demaine et al., 2009], which finds an equivalence between searches on a BST and point sets in the plane satisfying a certain property. To give an example of the utility of our approach, we introduce the log-interleave bound, a measure of the information-theoretic complexity of a permutation π, which is within a lg lg n multiplicative factor of a known lower bound in the BST model; we also devise a parallel sorting algorithm with polylogarithmic span that sorts a permutation π using comparisons proportional to its log-interleave bound. Our aforementioned result on sorting and offline BST algorithms can be used to show existence of an offline BST algorithm whose cost is within a constant factor of the log-interleave bound of any permutation π.

Cite as

Guy E. Blelloch and Magdalen Dobson. The Geometry of Tree-Based Sorting. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{blelloch_et_al:LIPIcs.ICALP.2023.26,
  author =	{Blelloch, Guy E. and Dobson, Magdalen},
  title =	{{The Geometry of Tree-Based Sorting}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{26:1--26:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.26},
  URN =		{urn:nbn:de:0030-drops-180780},
  doi =		{10.4230/LIPIcs.ICALP.2023.26},
  annote =	{Keywords: binary search trees, sorting, dynamic optimality, parallelism}
}

Document

DOI: 10.4230/LIPIcs.FORC.2023.1

From the Real Towards the Ideal: Risk Prediction in a Better World

Authors: Cynthia Dwork, Omer Reingold, and Guy N. Rothblum

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract

Prediction algorithms assign scores in [0,1] to individuals, often interpreted as "probabilities" of a positive outcome, for example, of repaying a loan or succeeding in a job. Success, however, rarely depends only on the individual: it is a function of the individual’s interaction with the environment, past and present. Environments do not treat all demographic groups equally. We initiate the study of corrective transformations τ that map predictors of success in the real world to predictors in a better world. In the language of algorithmic fairness, letting p^* denote the true probabilities of success in the real, unfair, world, we characterize the transformations τ for which it is feasible to find a predictor q̃ that is indistinguishable from τ(p^*). The problem is challenging because we do not have access to probabilities or even outcomes in a better world. Nor do we have access to probabilities p^* in the real world. The only data available for training are outcomes from the real world. We obtain a complete characterization of when it is possible to learn predictors that are indistinguishable from τ(p^*), in the form of a simple-to-state criterion describing necessary and sufficient conditions for doing so. This criterion is inextricably bound with the very existence of uncertainty.

Cite as

Cynthia Dwork, Omer Reingold, and Guy N. Rothblum. From the Real Towards the Ideal: Risk Prediction in a Better World. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dwork_et_al:LIPIcs.FORC.2023.1,
  author =	{Dwork, Cynthia and Reingold, Omer and Rothblum, Guy N.},
  title =	{{From the Real Towards the Ideal: Risk Prediction in a Better World}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.1},
  URN =		{urn:nbn:de:0030-drops-179224},
  doi =		{10.4230/LIPIcs.FORC.2023.1},
  annote =	{Keywords: Algorithmic Fairness, Affirmative Action, Learning, Predictions, Multicalibration, Outcome Indistinguishability}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.18

Certification with an NP Oracle

Authors: Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

In the certification problem, the algorithm is given a function f with certificate complexity k and an input x^⋆, and the goal is to find a certificate of size ≤ poly(k) for f’s value at x^⋆. This problem is in NP^NP, and assuming 𝖯 ≠ NP, is not in 𝖯. Prior works, dating back to Valiant in 1984, have therefore sought to design efficient algorithms by imposing assumptions on f such as monotonicity. Our first result is a BPP^NP algorithm for the general problem. The key ingredient is a new notion of the balanced influence of variables, a natural variant of influence that corrects for the bias of the function. Balanced influences can be accurately estimated via uniform generation, and classic BPP^NP algorithms are known for the latter task. We then consider certification with stricter instance-wise guarantees: for each x^⋆, find a certificate whose size scales with that of the smallest certificate for x^⋆. In sharp contrast with our first result, we show that this problem is NP^NP-hard even to approximate. We obtain an optimal inapproximability ratio, adding to a small handful of problems in the higher levels of the polynomial hierarchy for which optimal inapproximability is known. Our proof involves the novel use of bit-fixing dispersers for gap amplification.

Cite as

Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, and Li-Yang Tan. Certification with an NP Oracle. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{blanc_et_al:LIPIcs.ITCS.2023.18,
  author =	{Blanc, Guy and Koch, Caleb and Lange, Jane and Strassle, Carmen and Tan, Li-Yang},
  title =	{{Certification with an NP Oracle}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.18},
  URN =		{urn:nbn:de:0030-drops-175217},
  doi =		{10.4230/LIPIcs.ITCS.2023.18},
  annote =	{Keywords: Certificate complexity, Boolean functions, polynomial hierarchy, hardness of approximation}
}

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