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DOI: 10.4230/LIPIcs.CCC.2024.7

Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.

Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.35

Finer-Grained Hardness of Kernel Density Estimation

Authors: Josh Alman and Yunfeng Guan

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

In batch Kernel Density Estimation (KDE) for a kernel function f : ℝ^m × ℝ^m → ℝ, we are given as input 2n points x^{(1)}, …, x^{(n)}, y^{(1)}, …, y^{(n)} ∈ ℝ^m in dimension m, as well as a vector v ∈ ℝⁿ. These inputs implicitly define the n × n kernel matrix K given by K[i,j] = f(x^{(i)}, y^{(j)}). The goal is to compute a vector v ∈ ℝⁿ which approximates K w, i.e., with || Kw - v||_∞ < ε ||w||₁. For illustrative purposes, consider the Gaussian kernel f(x,y) : = e^{-||x-y||₂²}. The classic approach to this problem is the famous Fast Multipole Method (FMM), which runs in time n ⋅ O(log^m(ε^{-1})) and is particularly effective in low dimensions because of its exponential dependence on m. Recently, as the higher-dimensional case m ≥ Ω(log n) has seen more applications in machine learning and statistics, new algorithms have focused on this setting: an algorithm using discrepancy theory, which runs in time O(n / ε), and an algorithm based on the polynomial method, which achieves inverse polynomial accuracy in almost linear time when the input points have bounded square diameter B < o(log n). A recent line of work has proved fine-grained lower bounds, with the goal of showing that the "curse of dimensionality" arising in FMM is necessary assuming the Strong Exponential Time Hypothesis (SETH). Backurs et al. [NeurIPS 2017] first showed the hardness of a variety of Empirical Risk Minimization problems including KDE for Gaussian-like kernels in the case with high dimension m = Ω(log n) and large scale B = Ω(log n). Alman et al. [FOCS 2020] later developed new reductions in roughly this same parameter regime, leading to lower bounds for more general kernels, but only for very small error ε < 2^{- log^{Ω(1)} (n)}. In this paper, we refine the approach of Alman et al. to show new lower bounds in all parameter regimes, closing gaps between the known algorithms and lower bounds. For example: - In the setting where m = Clog n and B = o(log n), we prove Gaussian KDE requires n^{2-o(1)} time to achieve additive error ε < Ω(m/B)^{-m}, matching the performance of the polynomial method up to low-order terms. - In the low dimensional setting m = o(log n), we show that Gaussian KDE requires n^{2-o(1)} time to achieve ε such that log log (ε^{-1}) > ̃ Ω ((log n)/m), matching the error bound achievable by FMM up to low-order terms. To our knowledge, no nontrivial lower bound was previously known in this regime. Our approach also generalizes to any parameter regime and any kernel. For example, we achieve similar fine-grained hardness results for any kernel with slowly-decaying Taylor coefficients such as the Cauchy kernel. Our new lower bounds make use of an intricate analysis of the "counting matrix", a special case of the kernel matrix focused on carefully-chosen evaluation points. As a key technical lemma, we give a novel approach to bounding the entries of its inverse by using Schur polynomials from algebraic combinatorics.

Cite as

Josh Alman and Yunfeng Guan. Finer-Grained Hardness of Kernel Density Estimation. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 35:1-35:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{alman_et_al:LIPIcs.CCC.2024.35,
  author =	{Alman, Josh and Guan, Yunfeng},
  title =	{{Finer-Grained Hardness of Kernel Density Estimation}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{35:1--35:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.35},
  URN =		{urn:nbn:de:0030-drops-204311},
  doi =		{10.4230/LIPIcs.CCC.2024.35},
  annote =	{Keywords: Kernel Density Estimation, Fine-Grained Complexity, Schur Polynomials}
}

Document

DOI: 10.4230/LIPIcs.SEA.2024.15

Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs

Authors: Daniel Hambly, Rhyd Lewis, and Padraig Corcoran

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract

In this paper, we examine the NP-hard problem of identifying fixed-length s-t paths in edge-weighted graphs - that is, a path of a desired length k from a source vertex s to a target vertex t. Many existing strategies look at paths whose lengths are determined by the number of edges in the path. We, however, look at the length of the path as the sum of the edge weights. Here, three exact algorithms for this problem are proposed: the first based on an integer programming (IP) formulation, the second a backtracking algorithm, and the third based on an extension of Yen’s algorithm. Analysis of these algorithms on random graphs shows that the backtracking algorithm performs best on smaller values of k, whilst the IP is preferable for larger values of k.

Cite as

Daniel Hambly, Rhyd Lewis, and Padraig Corcoran. Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 15:1-15:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hambly_et_al:LIPIcs.SEA.2024.15,
  author =	{Hambly, Daniel and Lewis, Rhyd and Corcoran, Padraig},
  title =	{{Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{15:1--15:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.15},
  URN =		{urn:nbn:de:0030-drops-203805},
  doi =		{10.4230/LIPIcs.SEA.2024.15},
  annote =	{Keywords: Graphs, paths, backtracking, integer programming, Yen’s algorithm}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.39

Optimal Bounds for Distinct Quartics

Authors: Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

A fundamental concept related to strings is that of repetitions. It has been extensively studied in many versions, from both purely combinatorial and algorithmic angles. One of the most basic questions is how many distinct squares, i.e., distinct strings of the form UU, a string of length n can contain as fragments. It turns out that this is always 𝒪(n), and the bound cannot be improved to sublinear in n [Fraenkel and Simpson, JCTA 1998]. Several similar questions about repetitions in strings have been considered, and by now we seem to have a good understanding of their repetitive structure. For higher-dimensional strings, the basic concept of periodicity has been successfully extended and applied to design efficient algorithms - it is inherently more complex than for regular strings. Extending the notion of repetitions and understanding the repetitive structure of higher-dimensional strings is however far from complete. Quartics were introduced by Apostolico and Brimkov [TCS 2000] as analogues of squares in two dimensions. Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020] proved that the number of distinct quartics in an n×n 2D string is 𝒪(n²log²n) and that they can be computed in 𝒪(n²log²n) time. Gawrychowski, Ghazawi, and Landau [SPIRE 2021] constructed an infinite family of n×n 2D strings with Ω(n²log n) distinct quartics. This brings the challenge of determining asymptotically tight bounds. Here, we settle both the combinatorial and the algorithmic aspects of this question: the number of distinct quartics in an n×n 2D string is 𝒪(n²log n) and they can be computed in the worst-case optimal 𝒪(n²log n) time. As expected, our solution heavily exploits the periodic structure implied by occurrences of quartics. However, the two-dimensional nature of the problem introduces some technical challenges. Somewhat surprisingly, we overcome the final challenge for the combinatorial bound using a result of Marcus and Tardos [JCTA 2004] for permutation avoidance on matrices.

Cite as

Panagiotis Charalampopoulos, Paweł Gawrychowski, and Samah Ghazawi. Optimal Bounds for Distinct Quartics. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2024.39,
  author =	{Charalampopoulos, Panagiotis and Gawrychowski, Pawe{\l} and Ghazawi, Samah},
  title =	{{Optimal Bounds for Distinct Quartics}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.39},
  URN =		{urn:nbn:de:0030-drops-201823},
  doi =		{10.4230/LIPIcs.ICALP.2024.39},
  annote =	{Keywords: 2D strings, quartics, repetitions, periodicity}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.46

On the Streaming Complexity of Expander Decomposition

Authors: Yu Chen, Michael Kapralov, Mikhail Makarov, and Davide Mazzali

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

In this paper we study the problem of finding (ε, ϕ)-expander decompositions of a graph in the streaming model, in particular for dynamic streams of edge insertions and deletions. The goal is to partition the vertex set so that every component induces a ϕ-expander, while the number of inter-cluster edges is only an ε fraction of the total volume. It was recently shown that there exists a simple algorithm to construct a (O(ϕ log n), ϕ)-expander decomposition of an n-vertex graph using Õ(n/ϕ²) bits of space [Filtser, Kapralov, Makarov, ITCS'23]. This result calls for understanding the extent to which a dependence in space on the sparsity parameter ϕ is inherent. We move towards answering this question on two fronts. We prove that a (O(ϕ log n), ϕ)-expander decomposition can be found using Õ(n) space, for every ϕ. At the core of our result is the first streaming algorithm for computing boundary-linked expander decompositions, a recently introduced strengthening of the classical notion [Goranci et al., SODA'21]. The key advantage is that a classical sparsifier [Fung et al., STOC'11], with size independent of ϕ, preserves the cuts inside the clusters of a boundary-linked expander decomposition within a multiplicative error. Notable algorithmic applications use sequences of expander decompositions, in particular one often repeatedly computes a decomposition of the subgraph induced by the inter-cluster edges (e.g., the seminal work of Spielman and Teng on spectral sparsifiers [Spielman, Teng, SIAM Journal of Computing 40(4)], or the recent maximum flow breakthrough [Chen et al., FOCS'22], among others). We prove that any streaming algorithm that computes a sequence of (O(ϕ log n), ϕ)-expander decompositions requires Ω̃(n/ϕ) bits of space, even in insertion only streams.

Cite as

Yu Chen, Michael Kapralov, Mikhail Makarov, and Davide Mazzali. On the Streaming Complexity of Expander Decomposition. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2024.46,
  author =	{Chen, Yu and Kapralov, Michael and Makarov, Mikhail and Mazzali, Davide},
  title =	{{On the Streaming Complexity of Expander Decomposition}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.46},
  URN =		{urn:nbn:de:0030-drops-201890},
  doi =		{10.4230/LIPIcs.ICALP.2024.46},
  annote =	{Keywords: Graph Sketching, Dynamic Streaming, Expander Decomposition}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.57

Non-Linear Paging

Authors: Ilan Doron-Arad and Joseph (Seffi) Naor

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We formulate and study non-linear paging - a broad model of online paging where the size of subsets of pages is determined by a monotone non-linear set function of the pages. This model captures the well-studied classic weighted paging and generalized paging problems, and also submodular and supermodular paging, studied here for the first time, that have a range of applications from virtual memory to machine learning. Unlike classic paging, the cache threshold parameter k does not yield good competitive ratios for non-linear paging. Instead, we introduce a novel parameter 𝓁 that generalizes the notion of cache size to the non-linear setting. We obtain a tight deterministic 𝓁-competitive algorithm for general non-linear paging and a o(log²𝓁)-competitive lower bound for randomized algorithms. Our algorithm is based on a new generic LP for the problem that captures both submodular and supermodular paging, in contrast to LPs used for submodular cover settings. We finally focus on the supermodular paging problem, which is a variant of online set cover and online submodular cover, where sets are repeatedly requested to be removed from the cover. We obtain polylogarithmic lower and upper bounds and an offline approximation algorithm.

Cite as

Ilan Doron-Arad and Joseph (Seffi) Naor. Non-Linear Paging. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doronarad_et_al:LIPIcs.ICALP.2024.57,
  author =	{Doron-Arad, Ilan and Naor, Joseph (Seffi)},
  title =	{{Non-Linear Paging}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.57},
  URN =		{urn:nbn:de:0030-drops-202000},
  doi =		{10.4230/LIPIcs.ICALP.2024.57},
  annote =	{Keywords: paging, competitive analysis, non-linear paging, submodular and supermodular functions}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.153

On the Length of Strongly Monotone Descending Chains over ℕ^d

Authors: Sylvain Schmitz and Lia Schütze

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

A recent breakthrough by Künnemann, Mazowiecki, Schütze, Sinclair-Banks, and Węgrzycki (ICALP 2023) bounds the running time for the coverability problem in d-dimensional vector addition systems under unary encoding to n^{2^{O(d)}}, improving on Rackoff’s n^{2^{O(dlg d)}} upper bound (Theor. Comput. Sci. 1978), and provides conditional matching lower bounds. In this paper, we revisit Lazić and Schmitz' "ideal view" of the backward coverability algorithm (Inform. Comput. 2021) in the light of this breakthrough. We show that the controlled strongly monotone descending chains of downwards-closed sets over ℕ^d that arise from the dual backward coverability algorithm of Lazić and Schmitz on d-dimensional unary vector addition systems also enjoy this tight n^{2^{O(d)}} upper bound on their length, and that this also translates into the same bound on the running time of the backward coverability algorithm. Furthermore, our analysis takes place in a more general setting than that of Lazić and Schmitz, which allows to show the same results and improve on the 2EXPSPACE upper bound derived by Benedikt, Duff, Sharad, and Worrell (LICS 2017) for the coverability problem in invertible affine nets.

Cite as

Sylvain Schmitz and Lia Schütze. On the Length of Strongly Monotone Descending Chains over ℕ^d. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 153:1-153:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{schmitz_et_al:LIPIcs.ICALP.2024.153,
  author =	{Schmitz, Sylvain and Sch\"{u}tze, Lia},
  title =	{{On the Length of Strongly Monotone Descending Chains over \mathbb{N}^d}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{153:1--153:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.153},
  URN =		{urn:nbn:de:0030-drops-202964},
  doi =		{10.4230/LIPIcs.ICALP.2024.153},
  annote =	{Keywords: Vector addition system, coverability, well-quasi-order, order ideal, affine net}
}

Document

Survey

DOI: 10.4230/TGDK.2.1.1

Towards Representing Processes and Reasoning with Process Descriptions on the Web

Authors: Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract

We work towards a vocabulary to represent processes and temporal logic specifications as graph-structured data. Different fields use incompatible terminologies for describing essentially the same process-related concepts. In addition, processes can be represented from different perspectives and levels of abstraction: both state-centric and event-centric perspectives offer distinct insights into the underlying processes. In this work, we strive to unify the representation of processes and related concepts by leveraging the power of knowledge graphs. We survey approaches to representing processes and reasoning with process descriptions from different fields and provide a selection of scenarios to help inform the scope of a unified representation of processes. We focus on processes that can be executed and observed via web interfaces. We propose to provide a representation designed to combine state-centric and event-centric perspectives while incorporating temporal querying and reasoning capabilities on temporal logic specifications. A standardised vocabulary and representation for processes and temporal specifications would contribute towards bridging the gap between the terminologies from different fields and fostering the broader application of methods involving temporal logics, such as formal verification and program synthesis.

Cite as

Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese. Towards Representing Processes and Reasoning with Process Descriptions on the Web. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 1:1-1:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{harth_et_al:TGDK.2.1.1,
  author =	{Harth, Andreas and K\"{a}fer, Tobias and Rula, Anisa and Calbimonte, Jean-Paul and Kamburjan, Eduard and Giese, Martin},
  title =	{{Towards Representing Processes and Reasoning with Process Descriptions on the Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:32},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.1},
  URN =		{urn:nbn:de:0030-drops-198583},
  doi =		{10.4230/TGDK.2.1.1},
  annote =	{Keywords: Process modelling, Process ontology, Temporal logic, Web services}
}

Document

Position

DOI: 10.4230/TGDK.2.1.5

Standardizing Knowledge Engineering Practices with a Reference Architecture

Authors: Bradley P. Allen and Filip Ilievski

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract

Knowledge engineering is the process of creating and maintaining knowledge-producing systems. Throughout the history of computer science and AI, knowledge engineering workflows have been widely used given the importance of high-quality knowledge for reliable intelligent agents. Meanwhile, the scope of knowledge engineering, as apparent from its target tasks and use cases, has been shifting, together with its paradigms such as expert systems, semantic web, and language modeling. The intended use cases and supported user requirements between these paradigms have not been analyzed globally, as new paradigms often satisfy prior pain points while possibly introducing new ones. The recent abstraction of systemic patterns into a boxology provides an opening for aligning the requirements and use cases of knowledge engineering with the systems, components, and software that can satisfy them best, however, this direction has not been explored to date. This paper proposes a vision of harmonizing the best practices in the field of knowledge engineering by leveraging the software engineering methodology of creating reference architectures. We describe how a reference architecture can be iteratively designed and implemented to associate user needs with recurring systemic patterns, building on top of existing knowledge engineering workflows and boxologies. We provide a six-step roadmap that can enable the development of such an architecture, consisting of scope definition, selection of information sources, architectural analysis, synthesis of an architecture based on the information source analysis, evaluation through instantiation, and, ultimately, instantiation into a concrete software architecture. We provide an initial design and outcome of the definition of architectural scope, selection of information sources, and analysis. As the remaining steps of design, evaluation, and instantiation of the architecture are largely use-case specific, we provide a detailed description of their procedures and point to relevant examples. We expect that following through on this vision will lead to well-grounded reference architectures for knowledge engineering, will advance the ongoing initiatives of organizing the neurosymbolic knowledge engineering space, and will build new links to the software architectures and data science communities.

Cite as

Bradley P. Allen and Filip Ilievski. Standardizing Knowledge Engineering Practices with a Reference Architecture. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{allen_et_al:TGDK.2.1.5,
  author =	{Allen, Bradley P. and Ilievski, Filip},
  title =	{{Standardizing Knowledge Engineering Practices with a Reference Architecture}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:23},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.5},
  URN =		{urn:nbn:de:0030-drops-198623},
  doi =		{10.4230/TGDK.2.1.5},
  annote =	{Keywords: knowledge engineering, knowledge graphs, quality attributes, software architectures, sociotechnical systems}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2023.50

On Min-Max Graph Balancing with Strict Negative Correlation Constraints

Authors: Ting-Yu Kuo, Yu-Han Chen, Andrea Frosini, Sun-Yuan Hsieh, Shi-Chun Tsai, and Mong-Jen Kao

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract

We consider the min-max graph balancing problem with strict negative correlation (SNC) constraints. The graph balancing problem arises as an equivalent formulation of the classic unrelated machine scheduling problem, where we are given a hypergraph G = (V,E) with vertex-dependent edge weight function p: E×V ↦ ℤ^{≥0} that represents the processing time of the edges (jobs). The SNC constraints, which are given as edge subsets C_1,C_2,…,C_k, require that the edges in the same subset cannot be assigned to the same vertex at the same time. Under these constraints, the goal is to compute an edge orientation (assignment) that minimizes the maximum workload of the vertices. In this paper, we conduct a general study on the approximability of this problem. First, we show that, in the presence of SNC constraints, the case with max_{e ∈ E} |e| = max_i |C_i| = 2 is the only case for which approximation solutions can be obtained. Further generalization on either direction, e.g., max_{e ∈ E} |e| or max_i |C_i|, will directly make computing a feasible solution an NP-complete problem to solve. Then, we present a 2-approximation algorithm for the case with max_{e ∈ E} |e| = max_i |C_i| = 2, based on a set of structural simplifications and a tailored assignment LP for this problem. We note that our approach is general and can be applied to similar settings, e.g., scheduling with SNC constraints to minimize the weighted completion time, to obtain similar approximation guarantees. Further cases are discussed to describe the landscape of the approximability of this prbolem. For the case with |V| ≤ 2, which is already known to be NP-hard, we present a fully-polynomial time approximation scheme (FPTAS). On the other hand, we show that the problem is at least as hard as vertex cover to approximate when |V| ≥ 3.

Cite as

Ting-Yu Kuo, Yu-Han Chen, Andrea Frosini, Sun-Yuan Hsieh, Shi-Chun Tsai, and Mong-Jen Kao. On Min-Max Graph Balancing with Strict Negative Correlation Constraints. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kuo_et_al:LIPIcs.ISAAC.2023.50,
  author =	{Kuo, Ting-Yu and Chen, Yu-Han and Frosini, Andrea and Hsieh, Sun-Yuan and Tsai, Shi-Chun and Kao, Mong-Jen},
  title =	{{On Min-Max Graph Balancing with Strict Negative Correlation Constraints}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.50},
  URN =		{urn:nbn:de:0030-drops-193524},
  doi =		{10.4230/LIPIcs.ISAAC.2023.50},
  annote =	{Keywords: Unrelated Scheduling, Graph Balancing, Strict Correlation Constraints}
}

Document

DOI: 10.4230/LIPIcs.CSL.2022.14

Realising Intensional S4 and GL Modalities

Authors: Liang-Ting Chen and Hsiang-Shang Ko

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract

There have been investigations into type-theoretic foundations for metaprogramming, notably Davies and Pfenning’s (2001) treatment in S4 modal logic, where code evaluating to values of type A is given the modal type Code A (□A in the original paper). Recently Kavvos (2017) extended PCF with Code A and intensional recursion, understood as the deductive form of the GL (Gödel-Löb) axiom in provability logic, but the resulting type system is logically inconsistent. Inspired by staged computation, we observe that a term of type Code A is, in general, code to be evaluated in a next stage, whereas S4 modal type theory is a special case where code can be evaluated in the current stage, and the two types of code should be discriminated. Consequently, we use two separate modalities ⊠ and □ to model S4 and GL respectively in a unified categorical framework while retaining logical consistency. Following Kavvos’ (2017) novel approach to the semantics of intensionality, we interpret the two modalities in the P-category of assemblies and trackable maps. For the GL modality □ in particular, we use guarded type theory to articulate what it means by a “next” stage and to model intensional recursion by guarded recursion together with Kleene’s second recursion theorem. Besides validating the S4 and GL axioms, our model better captures the essence of intensionality by refuting congruence (so that two extensionally equal terms may not be intensionally equal) and internal quoting (both A → □A and A → ⊠A). Our results are developed in (guarded) homotopy type theory and formalised in Agda.

Cite as

Liang-Ting Chen and Hsiang-Shang Ko. Realising Intensional S4 and GL Modalities. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chen_et_al:LIPIcs.CSL.2022.14,
  author =	{Chen, Liang-Ting and Ko, Hsiang-Shang},
  title =	{{Realising Intensional S4 and GL Modalities}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.14},
  URN =		{urn:nbn:de:0030-drops-157341},
  doi =		{10.4230/LIPIcs.CSL.2022.14},
  annote =	{Keywords: provability, guarded recursion, realisability, modal types, metaprogramming}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2020.29

A Generalization of Self-Improving Algorithms

Authors: Siu-Wing Cheng, Man-Kwun Chiu, Kai Jin, and Man Ting Wong

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract

Ailon et al. [SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances x₁,⋯,x_n follow some unknown product distribution. That is, x_i comes from a fixed unknown distribution 𝒟_i, and the x_i’s are drawn independently. After spending O(n^{1+ε}) time in a learning phase, the subsequent expected running time is O((n+ H)/ε), where H ∈ {H_S,H_DT}, and H_S and H_DT are the entropies of the distributions of the sorting and DT output, respectively. In this paper, we allow dependence among the x_i’s under the group product distribution. There is a hidden partition of [1,n] into groups; the x_i’s in the k-th group are fixed unknown functions of the same hidden variable u_k; and the u_k’s are drawn from an unknown product distribution. We describe self-improving algorithms for sorting and DT under this model when the functions that map u_k to x_i’s are well-behaved. After an O(poly(n))-time training phase, we achieve O(n + H_S) and O(nα(n) + H_DT) expected running times for sorting and DT, respectively, where α(⋅) is the inverse Ackermann function.

Cite as

Siu-Wing Cheng, Man-Kwun Chiu, Kai Jin, and Man Ting Wong. A Generalization of Self-Improving Algorithms. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cheng_et_al:LIPIcs.SoCG.2020.29,
  author =	{Cheng, Siu-Wing and Chiu, Man-Kwun and Jin, Kai and Wong, Man Ting},
  title =	{{A Generalization of Self-Improving Algorithms}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.29},
  URN =		{urn:nbn:de:0030-drops-121873},
  doi =		{10.4230/LIPIcs.SoCG.2020.29},
  annote =	{Keywords: expected running time, entropy, sorting, Delaunay triangulation}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2018.29

A Dichotomy Result for Cyclic-Order Traversing Games

Authors: Yen-Ting Chen, Meng-Tsung Tsai, and Shi-Chun Tsai

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract

Traversing game is a two-person game played on a connected undirected simple graph with a source node and a destination node. A pebble is placed on the source node initially and then moves autonomously according to some rules. Alice is the player who wants to set up rules for each node to determine where to forward the pebble while the pebble reaches the node, so that the pebble can reach the destination node. Bob is the second player who tries to deter Alice's effort by removing edges. Given access to Alice's rules, Bob can remove as many edges as he likes, while retaining the source and destination nodes connected. Under the guide of Alice's rules, if the pebble arrives at the destination node, then we say Alice wins the traversing game; otherwise the pebble enters an endless loop without passing through the destination node, then Bob wins. We assume that Alice and Bob both play optimally. We study the problem: When will Alice have a winning strategy? This actually models a routing recovery problem in Software Defined Networking in which some links may be broken. In this paper, we prove a dichotomy result for certain traversing games, called cyclic-order traversing games. We also give a linear-time algorithm to find the corresponding winning strategy, if one exists.

Cite as

Yen-Ting Chen, Meng-Tsung Tsai, and Shi-Chun Tsai. A Dichotomy Result for Cyclic-Order Traversing Games. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2018.29,
  author =	{Chen, Yen-Ting and Tsai, Meng-Tsung and Tsai, Shi-Chun},
  title =	{{A Dichotomy Result for Cyclic-Order Traversing Games}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.29},
  URN =		{urn:nbn:de:0030-drops-99775},
  doi =		{10.4230/LIPIcs.ISAAC.2018.29},
  annote =	{Keywords: st-planar graphs, biconnectivity, fault-tolerant routing algorithms, software defined network}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2017.43

Eilenberg Theorems for Free

Authors: Henning Urbat, Jiri Adámek, Liang-Ting Chen, and Stefan Milius

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

Eilenberg-type correspondences, relating varieties of languages (e.g., of finite words, infinite words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic language theory. We show that they all arise from the same recipe: one models languages and the algebras recognizing them by monads on an algebraic category, and applies a Stone-type duality. Our main contribution is a variety theorem that covers e.g. Wilke's and Pin's work on infinity-languages, the variety theorem for cost functions of Daviaud, Kuperberg, and Pin, and unifies the two categorical approaches of Bojanczyk and of Adamek et al. In addition we derive new results, such as an extension of the local variety theorem of Gehrke, Grigorieff, and Pin from finite to infinite words.

Cite as

Henning Urbat, Jiri Adámek, Liang-Ting Chen, and Stefan Milius. Eilenberg Theorems for Free. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{urbat_et_al:LIPIcs.MFCS.2017.43,
  author =	{Urbat, Henning and Ad\'{a}mek, Jiri and Chen, Liang-Ting and Milius, Stefan},
  title =	{{Eilenberg Theorems for Free}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.43},
  URN =		{urn:nbn:de:0030-drops-81032},
  doi =		{10.4230/LIPIcs.MFCS.2017.43},
  annote =	{Keywords: Eilenberg's theorem, variety of languages, pseudovariety, monad, duality}
}

Document

DOI: 10.4230/LIPIcs.CALCO.2015.50

A Fibrational Approach to Automata Theory

Authors: Liang-Ting Chen and Henning Urbat

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract

For predual categories C and D we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids, respectively. As an application, a new proof of Eilenberg's variety theorem along with several related results is obtained, covering uniformly varieties of languages and their coalgebraic modifications, Straubing's C-varieties, and fully invariant local varieties.

Cite as

Liang-Ting Chen and Henning Urbat. A Fibrational Approach to Automata Theory. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 50-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{chen_et_al:LIPIcs.CALCO.2015.50,
  author =	{Chen, Liang-Ting and Urbat, Henning},
  title =	{{A Fibrational Approach to Automata Theory}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{50--65},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.50},
  URN =		{urn:nbn:de:0030-drops-55268},
  doi =		{10.4230/LIPIcs.CALCO.2015.50},
  annote =	{Keywords: Eilenberg’s variety theorem, duality, coalgebra, Grothendieck fibration}
}

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