DROPS

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DOI: 10.4230/LIPIcs.DISC.2024.9

Freeze-Tag in L₁ Has Wake-Up Time Five with Linear Complexity

Authors: Nicolas Bonichon, Arnaud Casteigts, Cyril Gavoille, and Nicolas Hanusse

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

Abstract

The Freeze-Tag Problem, introduced in Arkin et al. (SODA'02) consists of waking up a swarm of n robots, starting from a single active robot. In the basic geometric version, every robot is given coordinates in the plane. As soon as a robot is awakened, it can move towards inactive robots to wake them up. The goal is to minimize the makespan of the last robot, the makespan. Despite significant progress on the computational complexity of this problem and on approximation algorithms, the characterization of exact bounds on the makespan remains one of the main open questions. In this paper, we settle this question for the 𝓁₁-norm, showing that a makespan of at most 5r can always be achieved, where r is the maximum distance between the initial active robot and any sleeping robot. Moreover, a schedule achieving a makespan of at most 5r can be computed in time O(n). Both bounds, the time and the makespan are optimal. Our results also imply for the 𝓁₂-norm a new upper bound of 5√2r ≈ 7.07r on the makespan, improving the best known bound of (5+2√2+√5)r ≈ 10.06r. Along the way, we introduce new linear time wake-up strategies, that apply to any norm and show that an optimal bound on the makespan can always be achieved by a schedule computable in linear time.

Cite as

Nicolas Bonichon, Arnaud Casteigts, Cyril Gavoille, and Nicolas Hanusse. Freeze-Tag in L₁ Has Wake-Up Time Five with Linear Complexity. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonichon_et_al:LIPIcs.DISC.2024.9,
  author =	{Bonichon, Nicolas and Casteigts, Arnaud and Gavoille, Cyril and Hanusse, Nicolas},
  title =	{{Freeze-Tag in L₁ Has Wake-Up Time Five with Linear Complexity}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{9:1--9:16},
  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.2024.9},
  URN =		{urn:nbn:de:0030-drops-212356},
  doi =		{10.4230/LIPIcs.DISC.2024.9},
  annote =	{Keywords: freeze-tag problem, metric, algorithm}
}

Document

DOI: 10.4230/LIPIcs.ESA.2024.7

Segment Proximity Graphs and Nearest Neighbor Queries Amid Disjoint Segments

Authors: Pankaj K. Agarwal, Haim Kaplan, Matthew J. Katz, and Micha Sharir

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

In this paper we study a few proximity problems related to a set of pairwise-disjoint segments in {ℝ}². Let S be a set of n pairwise-disjoint segments in {ℝ}², and let r > 0 be a parameter. We define the segment proximity graph of S to be G_r(S) := (S,E), where E = {(e₁,e₂) ∣ dist(e₁,e₂) ≤ r} and dist (e₁,e₂) = min_{(p,q) ∈ e₁× e₂} ‖p-q‖ is the Euclidean distance between e₁ and e₂. We define the weight of an edge (e₁,e₂) ∈ E to be dist(e₁,e₂). We first present a simple grid-based O(nlog² n)-time algorithm for computing a BFS tree of G_r(S). We apply it to obtain an O^*(n^{6/5}) + O(nlog²nlogΔ)-time algorithm for the so-called reverse shortest path problem, in which we want to find the smallest value r^* for which G_{r^*}(S) contains a path of some specified length between two designated start and target segments (where the O^*(⋅) notation hides polylogarithmic factors). Here Δ = max_{e ≠ e' ∈ S} dist(e,e')/min_{e ≠ e' ∈ S} dist(e,e') is the spread of S. Next, we present a dynamic data structure that can maintain a set S of pairwise-disjoint segments in the plane under insertions/deletions, so that, for a query segment e from an unknown set Q of pairwise-disjoint segments, such that e does not intersect any segment in (the current version of) S, the segment of S closest to e can be computed in O(log⁵ n) amortized time. The amortized update time is also O(log⁵ n). We note that if the segments in S∪Q are allowed to intersect then the known lower bounds on halfplane range searching suggest that a sequence of n updates and queries may take at least close to Ω(n^{4/3}) time. One thus has to strongly rely on the non-intersecting property of S and Q to perform updates and queries in O(polylog(n)) (amortized) time each. Using these results on nearest-neighbor (NN) searching for disjoint segments, we show that a DFS tree (or forest) of G_r(S) can be computed in O^*(n) time. We also obtain an O^*(n)-time algorithm for constructing a minimum spanning tree of G_r(S). Finally, we present an O^*(n^{4/3})-time algorithm for computing a single-source shortest-path tree in G_r(S). This is the only result that does not exploit the disjointness of the input segments.

Cite as

Pankaj K. Agarwal, Haim Kaplan, Matthew J. Katz, and Micha Sharir. Segment Proximity Graphs and Nearest Neighbor Queries Amid Disjoint Segments. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{agarwal_et_al:LIPIcs.ESA.2024.7,
  author =	{Agarwal, Pankaj K. and Kaplan, Haim and Katz, Matthew J. and Sharir, Micha},
  title =	{{Segment Proximity Graphs and Nearest Neighbor Queries Amid Disjoint Segments}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.7},
  URN =		{urn:nbn:de:0030-drops-210782},
  doi =		{10.4230/LIPIcs.ESA.2024.7},
  annote =	{Keywords: segment proximity graphs, nearest neighbor searching, dynamic data structures, BFS, DFS, unit-disk graphs}
}

Document

DOI: 10.4230/LIPIcs.ESA.2024.28

A Faster Algorithm for the Fréchet Distance in 1D for the Imbalanced Case

Authors: Lotte Blank and Anne Driemel

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

The fine-grained complexity of computing the {Fréchet distance } has been a topic of much recent work, starting with the quadratic SETH-based conditional lower bound by Bringmann from 2014. Subsequent work established largely the same complexity lower bounds for the {Fréchet distance } in 1D. However, the imbalanced case, which was shown by Bringmann to be tight in dimensions d ≥ 2, was still left open. Filling in this gap, we show that a faster algorithm for the {Fréchet distance } in the imbalanced case is possible: Given two 1-dimensional curves of complexity n and n^{α} for some α ∈ (0,1), we can compute their {Fréchet distance } in O(n^{2α} log² n + n log n) time. This rules out a conditional lower bound of the form O((nm)^{1-ε}) that Bringmann showed for d ≥ 2 and any ε > 0 in turn showing a strict separation with the setting d = 1. At the heart of our approach lies a data structure that stores a 1-dimensional curve P of complexity n, and supports queries with a curve Q of complexity m for the continuous {Fréchet distance } between P and Q. The data structure has size in 𝒪(nlog n) and uses query time in 𝒪(m² log² n). Our proof uses a key lemma that is based on the concept of visiting orders and may be of independent interest. We demonstrate this by substantially simplifying the correctness proof of a clustering algorithm by Driemel, Krivošija and Sohler from 2015.

Cite as

Lotte Blank and Anne Driemel. A Faster Algorithm for the Fréchet Distance in 1D for the Imbalanced Case. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blank_et_al:LIPIcs.ESA.2024.28,
  author =	{Blank, Lotte and Driemel, Anne},
  title =	{{A Faster Algorithm for the Fr\'{e}chet Distance in 1D for the Imbalanced Case}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.28},
  URN =		{urn:nbn:de:0030-drops-210999},
  doi =		{10.4230/LIPIcs.ESA.2024.28},
  annote =	{Keywords: \{Fr\'{e}chet distance\}, distance oracle, data structures, time series}
}

Document

DOI: 10.4230/LIPIcs.ESA.2024.66

Shortest Path Separators in Unit Disk Graphs

Authors: Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighbourhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths.

Cite as

Elfarouk Harb, Zhengcheng Huang, and Da Wei Zheng. Shortest Path Separators in Unit Disk Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harb_et_al:LIPIcs.ESA.2024.66,
  author =	{Harb, Elfarouk and Huang, Zhengcheng and Zheng, Da Wei},
  title =	{{Shortest Path Separators in Unit Disk Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.66},
  URN =		{urn:nbn:de:0030-drops-211375},
  doi =		{10.4230/LIPIcs.ESA.2024.66},
  annote =	{Keywords: Balanced shortest path separators, unit disk graphs, crossings}
}

Document

DOI: 10.4230/LIPIcs.AFT.2024.25

Adaptive Curves for Optimally Efficient Market Making

Authors: Viraj Nadkarni, Sanjeev Kulkarni, and Pramod Viswanath

Published in: LIPIcs, Volume 316, 6th Conference on Advances in Financial Technologies (AFT 2024)

Abstract

Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bonding curves to trader behavior, based on the classical market microstructure model of Glosten and Milgrom. Our approach ensures a zero-profit condition for the market maker’s prices. We derive the differential equation that an optimal adaptive curve should follow to minimize arbitrage losses while remaining competitive. Solutions to this optimality equation are obtained for standard Gaussian and Lognormal price models using Kalman filtering. A key feature of our method is its ability to estimate the external market price without relying on price or loss oracles. We also provide an equivalent differential equation for the implied dynamics of canonical static bonding curves and establish conditions for their optimality. Our algorithms demonstrate robustness to changing market conditions and adversarial perturbations, and we offer an on-chain implementation using Uniswap v4 alongside off-chain AI co-processors.

Cite as

Viraj Nadkarni, Sanjeev Kulkarni, and Pramod Viswanath. Adaptive Curves for Optimally Efficient Market Making. In 6th Conference on Advances in Financial Technologies (AFT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 316, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{nadkarni_et_al:LIPIcs.AFT.2024.25,
  author =	{Nadkarni, Viraj and Kulkarni, Sanjeev and Viswanath, Pramod},
  title =	{{Adaptive Curves for Optimally Efficient Market Making}},
  booktitle =	{6th Conference on Advances in Financial Technologies (AFT 2024)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-345-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{316},
  editor =	{B\"{o}hme, Rainer and Kiffer, Lucianna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2024.25},
  URN =		{urn:nbn:de:0030-drops-209612},
  doi =		{10.4230/LIPIcs.AFT.2024.25},
  annote =	{Keywords: Automated market makers, Adaptive, Glosten-Milgrom, Decentralized Finance}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2024.15

Rose: Composable Autodiff for the Interactive Web

Authors: Sam Estep, Wode Ni, Raven Rothkopf, and Joshua Sunshine

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract

Reverse-mode automatic differentiation (autodiff) has been popularized by deep learning, but its ability to compute gradients is also valuable for interactive use cases such as bidirectional computer-aided design, embedded physics simulations, visualizing causal inference, and more. Unfortunately, the web is ill-served by existing autodiff frameworks, which use autodiff strategies that perform poorly on dynamic scalar programs, and pull in heavy dependencies that would result in unacceptable webpage sizes. This work introduces Rose, a lightweight autodiff framework for the web using a new hybrid approach to reverse-mode autodiff, blending conventional tracing and transformation techniques in a way that uses the host language for metaprogramming while also allowing the programmer to explicitly define reusable functions that comprise a larger differentiable computation. We demonstrate the value of the Rose design by porting two differentiable physics simulations, and evaluate its performance on an optimization-based diagramming application, showing Rose outperforming the state-of-the-art in web-based autodiff by multiple orders of magnitude.

Cite as

Sam Estep, Wode Ni, Raven Rothkopf, and Joshua Sunshine. Rose: Composable Autodiff for the Interactive Web. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 15:1-15:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{estep_et_al:LIPIcs.ECOOP.2024.15,
  author =	{Estep, Sam and Ni, Wode and Rothkopf, Raven and Sunshine, Joshua},
  title =	{{Rose: Composable Autodiff for the Interactive Web}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{15:1--15:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.15},
  URN =		{urn:nbn:de:0030-drops-208642},
  doi =		{10.4230/LIPIcs.ECOOP.2024.15},
  annote =	{Keywords: Automatic differentiation, differentiable programming, compilers, web}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2024.22

Constrictor: Immutability as a Design Concept

Authors: Elad Kinsbruner, Shachar Itzhaky, and Hila Peleg

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract

Many object-oriented applications in algorithm design rely on objects never changing during their lifetime. This is often tackled by marking object references as read-only, e.g., using the const keyword in C++. In other languages like Python or Java where such a concept does not exist, programmers rely on best practices that are entirely unenforced. While reliance on best practices is obviously too permissive, const-checking is too restrictive: it is possible for a method to mutate the internal state while still satisfying the property we expect from an "immutable" object in this setting. We would therefore like to enforce the immutability of an object’s abstract state. We check an object’s immutability through a view of its abstract state: for instances of an immutable class, the view does not change when running any of the class’s methods, even if some of the internal state does change. If all methods of a class are verified as non-mutating, we can deem the entire class view-immutable. We present an SMT-based algorithm to check view-immutability, and implement it in our linter/verifier, Constrictor. We evaluate Constrictor on 51 examples of immutability-related design violations. Our evaluation shows that Constrictor is effective at catching a variety of prototypical design violations, and does so in seconds. We also explore Constrictor with two real-world case studies.

Cite as

Elad Kinsbruner, Shachar Itzhaky, and Hila Peleg. Constrictor: Immutability as a Design Concept. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 22:1-22:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kinsbruner_et_al:LIPIcs.ECOOP.2024.22,
  author =	{Kinsbruner, Elad and Itzhaky, Shachar and Peleg, Hila},
  title =	{{Constrictor: Immutability as a Design Concept}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{22:1--22:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.22},
  URN =		{urn:nbn:de:0030-drops-208715},
  doi =		{10.4230/LIPIcs.ECOOP.2024.22},
  annote =	{Keywords: Immutability, Design Enforcement, SMT, Liskov Substitution Principle, Object-oriented Programming}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2024.33

Compiling with Arrays

Authors: David Richter, Timon Böhler, Pascal Weisenburger, and Mira Mezini

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract

Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time access and bulk operations. To bridge this gap, some languages represent arrays as (eager) functions instead of lists. In this paper, we connect this idea to a formal logical foundation by interpreting functions as the usual negative types from polarized type theory, and arrays as the corresponding dual positive version of the function type. Positive types are defined to have a single elimination form whose computational interpretation is pattern matching. Just like (positive) product types bind two variables during pattern matching, (positive) array types bind variables with multiplicity during pattern matching. We follow a similar approach for Booleans by introducing conditionally-defined variables. The positive formulation for the array type enables us to combine typed partial evaluation and common subexpression elimination into an elegant algorithm whose result enjoys a property we call maximal fission, which we argue can be beneficial for further optimizations. For this purpose, we present the novel intermediate representation indexed administrative normal form (A_{i}NF), which relies on the formal logical foundation of the positive formulation for the array type to facilitate maximal loop fission and subsequent optimizations. A_{i}NF is normal with regard to commuting conversion for both let-bindings and for-loops, leading to flat and maximally fissioned terms. We mechanize the translation and normalization from a simple surface language to A_{i}NF, establishing that the process terminates, preserves types, and produces maximally fissioned terms.

Cite as

David Richter, Timon Böhler, Pascal Weisenburger, and Mira Mezini. Compiling with Arrays. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{richter_et_al:LIPIcs.ECOOP.2024.33,
  author =	{Richter, David and B\"{o}hler, Timon and Weisenburger, Pascal and Mezini, Mira},
  title =	{{Compiling with Arrays}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.33},
  URN =		{urn:nbn:de:0030-drops-208823},
  doi =		{10.4230/LIPIcs.ECOOP.2024.33},
  annote =	{Keywords: array languages, functional programming, domain-specific languages, normalization by evaluation, common subexpression elimination, polarity, positive function type, intrinsic types}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2024.42

Failure Transparency in Stateful Dataflow Systems

Authors: Aleksey Veresov, Jonas Spenger, Paris Carbone, and Philipp Haller

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract

Failure transparency enables users to reason about distributed systems at a higher level of abstraction, where complex failure-handling logic is hidden. This is especially true for stateful dataflow systems, which are the backbone of many cloud applications. In particular, this paper focuses on proving failure transparency in Apache Flink, a popular stateful dataflow system. Even though failure transparency is a critical aspect of Apache Flink, to date it has not been formally proven. Showing that the failure transparency mechanism is correct, however, is challenging due to the complexity of the mechanism itself. Nevertheless, this complexity can be effectively hidden behind a failure transparent programming interface. To show that Apache Flink is failure transparent, we model it in small-step operational semantics. Next, we provide a novel definition of failure transparency based on observational explainability, a concept which relates executions according to their observations. Finally, we provide a formal proof of failure transparency for the implementation model; i.e., we prove that the failure-free model correctly abstracts from the failure-related details of the implementation model. We also show liveness of the implementation model under a fair execution assumption. These results are a first step towards a verified stack for stateful dataflow systems.

Cite as

Aleksey Veresov, Jonas Spenger, Paris Carbone, and Philipp Haller. Failure Transparency in Stateful Dataflow Systems. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 42:1-42:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{veresov_et_al:LIPIcs.ECOOP.2024.42,
  author =	{Veresov, Aleksey and Spenger, Jonas and Carbone, Paris and Haller, Philipp},
  title =	{{Failure Transparency in Stateful Dataflow Systems}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{42:1--42:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.42},
  URN =		{urn:nbn:de:0030-drops-208911},
  doi =		{10.4230/LIPIcs.ECOOP.2024.42},
  annote =	{Keywords: Failure transparency, stateful dataflow, operational semantics, checkpoint recovery}
}

Document

DOI: 10.4230/LIPIcs.DNA.30.1

Geometric Enumeration of Localized DNA Strand Displacement Reaction Networks

Authors: Matthew R. Lakin and Sarika Kumar

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract

Localized molecular devices are a powerful tool for engineering complex information-processing circuits and molecular robots. Their practical advantages include speed and scalability of interactions between components tethered near to each other on an underlying nanostructure, and the ability to restrict interactions between more distant components. The latter is a critical feature that must be factored into computational tools for the design and simulation of localized molecular devices: unlike in solution-phase systems, the geometries of molecular interactions must be accounted for when attempting to determine the network of possible reactions in a tethered molecular system. This work aims to address that challenge by integrating, for the first time, automated approaches to analysis of molecular geometry with reaction enumeration algorithms for DNA strand displacement reaction networks that can be applied to tethered molecular systems. By adapting a simple approach to solving the biophysical constraints inherent in molecular interactions to be applicable to tethered systems, we produce a localized reaction enumeration system that enhances previous approaches to reaction enumeration in tethered system by not requiring users to explicitly specify the subsets of components that are capable of interacting. This greatly simplifies the user’s task and could also be used as the basis of future systems for automated placement or routing of signal-transmission and logical processing in molecular devices. We apply this system to several published example systems from the literature, including both tethered molecular logic systems and molecular robots.

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Matthew R. Lakin and Sarika Kumar. Geometric Enumeration of Localized DNA Strand Displacement Reaction Networks. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lakin_et_al:LIPIcs.DNA.30.1,
  author =	{Lakin, Matthew R. and Kumar, Sarika},
  title =	{{Geometric Enumeration of Localized DNA Strand Displacement Reaction Networks}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.1},
  URN =		{urn:nbn:de:0030-drops-209294},
  doi =		{10.4230/LIPIcs.DNA.30.1},
  annote =	{Keywords: Localized circuits, reaction enumeration, DNA strand displacement, geometry, molecular computing}
}

Document

DOI: 10.4230/LIPIcs.DNA.30.2

Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds

Authors: Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, and Damien Woods

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract

Molecular programmers and nanostructure engineers use domain-level design to abstract away messy DNA/RNA sequence, chemical and geometric details. Such domain-level abstractions are enforced by sequence design principles and provide a key principle that allows scaling up of complex multistranded DNA/RNA programs and structures. Determining the most favoured secondary structure, or Minimum Free Energy (MFE), of a set of strands, is typically studied at the sequence level but has seen limited domain-level work. We analyse the computational complexity of MFE for multistranded systems in a simple setting were we allow only 1 or 2 domains per strand. On the one hand, with 2-domain strands, we find that the MFE decision problem is NP-complete, even without pseudoknots, and requires exponential time algorithms assuming SAT does. On the other hand, in the simplest case of 1-domain strands there are efficient MFE algorithms for various binding modes. However, even in this single-domain case, MFE is P-hard for promiscuous binding, where one domain may bind to multiple as experimentally used by Nikitin [Nat Chem., 2023], which in turn implies that strands consisting of a single domain efficiently implement arbitrary Boolean circuits.

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Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, and Damien Woods. Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{demaine_et_al:LIPIcs.DNA.30.2,
  author =	{Demaine, Erik D. and Gomez, Timothy and Grizzell, Elise and Hecher, Markus and Lynch, Jayson and Schweller, Robert and Shalaby, Ahmed and Woods, Damien},
  title =	{{Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{2:1--2:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.2},
  URN =		{urn:nbn:de:0030-drops-209304},
  doi =		{10.4230/LIPIcs.DNA.30.2},
  annote =	{Keywords: Domain-based DNA designs, minimum free energy, efficient algorithms, NP-hard, P-hard, NC, fixed-parameter tractable}
}

@InProceedings{demaine_et_al:LIPIcs.DNA.30.2,
  author =	{Demaine, Erik D. and Gomez, Timothy and Grizzell, Elise and Hecher, Markus and Lynch, Jayson and Schweller, Robert and Shalaby, Ahmed and Woods, Damien},
  title =	{{Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{2:1--2:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.2},
  URN =		{urn:nbn:de:0030-drops-209304},
  doi =		{10.4230/LIPIcs.DNA.30.2},
  annote =	{Keywords: Domain-based DNA designs, minimum free energy, efficient algorithms, NP-hard, P-hard, NC, fixed-parameter tractable}
}

Document

DOI: 10.4230/LIPIcs.DNA.30.3

Simulation of the Abstract Tile Assembly Model Using Crisscross Slats

Authors: Phillip Drake, Daniel Hader, and Matthew J. Patitz

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract

The abstract Tile Assembly Model (aTAM) provides an excellent foundation for the mathematical study of DNA-tile-based self-assembling systems, especially those wherein logic is embedded within the designs of the tiles so that they follow prescribed algorithms. While such algorithmic self-assembling systems are theoretically powerful, being computationally universal and capable of building complex shapes using information-theoretically optimal numbers of tiles, physical DNA-based implementations of these systems still encounter formidable error rates and undesired nucleation that hinder this theoretical potential. Slat-based self-assembly is a recent development wherein DNA forms long slats that combine together in 2 layers, rather than square tiles in a plane. In this approach, the length of the slats is key; while tiles typically only bind to 2 neighboring tiles at a time, slats may bind to dozens of other slats. This increased coordination between slats means that several mismatched slats must coincidentally meet in just the right way for errors to persist, unlike tiles where only a few are required. Consequently, while still a novel technology, large slat-based DNA constructions have been successfully implemented in the lab with resilience to many tile-based construction problems. These improved error characteristics come at a cost however, as slat-based systems are often more difficult to design and simulate than tile-based ones. Moreover, it has not been clear whether slats, with their larger sizes and different geometries, have the same theoretical capabilities as tiles. In this paper, we show that slats are capable of doing anything that tiles can, at least at scale. We demonstrate that any aTAM system may be converted to and simulated by an effectively equivalent system of slats. Furthermore, we show that these simulating slat systems can be made more efficiently, using shorter slats and a smaller scale factor, if the simulated tile system avoids certain uncommon growth patterns. Specifically, we consider 5 classes of aTAM systems with increasing complexity, from zig-zag systems which grow in a rigid pattern to the full class of all aTAM systems, and show how they may be converted to equivalent slat systems. We show that the simplest class may be simulated by slats at only a 2c × 2c scale, where c is the freely chosen coordination number of the slats, and further show that the full class of aTAM systems can be simulated at only a 5c × 5c scale. These results prove that slats have the full theoretical power of aTAM tiles while also providing constructions that are compact enough for potential DNA-based implementations of slat systems that are both capable of powerful algorithmic self-assembly and possessing of the strong error resilience of slats.

Cite as

Phillip Drake, Daniel Hader, and Matthew J. Patitz. Simulation of the Abstract Tile Assembly Model Using Crisscross Slats. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 3:1-3:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{drake_et_al:LIPIcs.DNA.30.3,
  author =	{Drake, Phillip and Hader, Daniel and Patitz, Matthew J.},
  title =	{{Simulation of the Abstract Tile Assembly Model Using Crisscross Slats}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{3:1--3:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.3},
  URN =		{urn:nbn:de:0030-drops-209315},
  doi =		{10.4230/LIPIcs.DNA.30.3},
  annote =	{Keywords: DNA origami, tile-assembly, self-assembly, aTAM, kinetic modeling, computational modeling}
}

Document

DOI: 10.4230/LIPIcs.WABI.2024.6

Cosine Similarity Estimation Using FracMinHash: Theoretical Analysis, Safety Conditions, and Implementation

Authors: Mahmudur Rahman Hera and David Koslicki

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract

Motivation. The increasing number and volume of genomic and metagenomic data necessitates scalable and robust computational models for precise analysis. Sketching techniques utilizing k-mers from a biological sample have proven to be useful for large-scale analyses. In recent years, FracMinHash has emerged as a popular sketching technique and has been used in several useful applications. Recent studies on FracMinHash proved unbiased estimators for the containment and Jaccard indices. However, theoretical investigations for other metrics, such as the cosine similarity, are still lacking. Theoretical contributions. In this paper, we present a theoretical framework for estimating cosine similarity from FracMinHash sketches. We establish conditions under which this estimation is sound, and recommend a minimum scale factor s for accurate results. Experimental evidence supports our theoretical findings. Practical contributions. We also present frac-kmc, a fast and efficient FracMinHash sketch generator program. frac-kmc is the fastest known FracMinHash sketch generator, delivering accurate and precise results for cosine similarity estimation on real data. We show that by computing FracMinHash sketches using frac-kmc, we can estimate pairwise cosine similarity speedily and accurately on real data. frac-kmc is freely available here: https://github.com/KoslickiLab/frac-kmc/.

Cite as

Mahmudur Rahman Hera and David Koslicki. Cosine Similarity Estimation Using FracMinHash: Theoretical Analysis, Safety Conditions, and Implementation. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hera_et_al:LIPIcs.WABI.2024.6,
  author =	{Hera, Mahmudur Rahman and Koslicki, David},
  title =	{{Cosine Similarity Estimation Using FracMinHash: Theoretical Analysis, Safety Conditions, and Implementation}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.6},
  URN =		{urn:nbn:de:0030-drops-206502},
  doi =		{10.4230/LIPIcs.WABI.2024.6},
  annote =	{Keywords: Hashing, sketching, FracMinHash, Min-Hash, k-mer, similarity, theory}
}

Document

DOI: 10.4230/LIPIcs.WABI.2024.23

AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction

Authors: Adam Cicherski, Anna Lisiecka, and Norbert Dojer

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract

The success of pangenome-based approaches to genomics analysis depends largely on the existence of efficient methods for constructing pangenome graphs that are applicable to large genome collections. In the current paper we present AlfaPang, a new pangenome graph building algorithm. AlfaPang is based on a novel alignment-free approach that allows to construct pangenome graphs using significantly less computational resources than state-of-the-art tools. The code of AlfaPang is freely available at https://github.com/AdamCicherski/AlfaPang.

Cite as

Adam Cicherski, Anna Lisiecka, and Norbert Dojer. AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cicherski_et_al:LIPIcs.WABI.2024.23,
  author =	{Cicherski, Adam and Lisiecka, Anna and Dojer, Norbert},
  title =	{{AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.23},
  URN =		{urn:nbn:de:0030-drops-206673},
  doi =		{10.4230/LIPIcs.WABI.2024.23},
  annote =	{Keywords: pangenome, variation graph, genome alignment, population genomics}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2024.6

Monotonicity of the Cops and Robber Game for Bounded Depth Treewidth

Authors: Isolde Adler and Eva Fluck

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

Abstract

We study a variation of the cops and robber game characterising treewidth, where in each round at most one cop may be placed and in each play at most q rounds are played, where q is a parameter of the game. We prove that if k cops have a winning strategy in this game, then k cops have a monotone winning strategy. As a corollary we obtain a new characterisation of bounded depth treewidth, and we give a positive answer to an open question by Fluck, Seppelt and Spitzer (2024), thus showing that graph classes of bounded depth treewidth are homomorphism distinguishing closed. Our proof of monotonicity substantially reorganises a winning strategy by first transforming it into a pre-tree decomposition, which is inspired by decompositions of matroids, and then applying an intricate breadth-first "cleaning up" procedure along the pre-tree decomposition (which may temporarily lose the property of representing a strategy), in order to achieve monotonicity while controlling the number of rounds simultaneously across all branches of the decomposition via a vertex exchange argument. We believe this can be useful in future research.

Cite as

Isolde Adler and Eva Fluck. Monotonicity of the Cops and Robber Game for Bounded Depth Treewidth. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{adler_et_al:LIPIcs.MFCS.2024.6,
  author =	{Adler, Isolde and Fluck, Eva},
  title =	{{Monotonicity of the Cops and Robber Game for Bounded Depth Treewidth}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{6:1--6:18},
  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.2024.6},
  URN =		{urn:nbn:de:0030-drops-205621},
  doi =		{10.4230/LIPIcs.MFCS.2024.6},
  annote =	{Keywords: tree decompositions, treewidth, treedepth, cops-and-robber game, monotonicity, homomorphism distinguishing closure}
}

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