DROPS

Document

DOI: 10.4230/LIPIcs.SWAT.2026.19

Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means

Authors: Nicole Funk, Annika Hennes, Johanna Hillebrand, and Sarah Sturm

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

We study discrete k-clustering problems in general metric spaces that are constrained by a combination of two different fairness conditions within the demographic fairness model. Given a metric space (P,d), where every point in P is equipped with a protected attribute, and a number k, the goal is to partition P into k clusters with a designated center each, such that a center-based objective function is minimized and the attributes are fairly distributed with respect to the following two fairness concepts: 1) group fairness: We aim for clusters with balanced numbers of attributes by specifying lower and upper bounds for the desired attribute proportions. 2) diverse center selection: Clusters have natural representatives, i.e., their centers. We ask for a balanced set of representatives by specifying the desired number of centers to choose from each attribute. Dickerson, Esmaeili, Morgenstern, and Pena [John P. Dickerson et al., 2023] denote the combination of these two constraints as doubly constrained fair clustering. They present algorithms whose guarantees depend on the best known approximation factors for either of these problems. Currently, this implies an 8-approximation with a small additive violation on the group fairness constraint. For k-center, we improve this approximation factor to 4 with a small additive violation. This guarantee also depends on the currently best algorithm for DS-fair k-center given by Jones, Nguyen and Nguyen [Matthew Jones et al., 2020]. For k-median and k-means, we propose the first constant-factor approximation algorithms. Our algorithms transform a solution that satisfies diverse center selection into a doubly constrained fair clustering using an LP-based approach. Furthermore, our results are generalizable to other center-selection constraints, such as matroid k-clustering and knapsack constraints.

Cite as

Nicole Funk, Annika Hennes, Johanna Hillebrand, and Sarah Sturm. Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{funk_et_al:LIPIcs.SWAT.2026.19,
  author =	{Funk, Nicole and Hennes, Annika and Hillebrand, Johanna and Sturm, Sarah},
  title =	{{Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.19},
  URN =		{urn:nbn:de:0030-drops-260551},
  doi =		{10.4230/LIPIcs.SWAT.2026.19},
  annote =	{Keywords: Clustering, Fairness, Approximation Algorithms, k-center, k-median, k-means}
}

Document

Research

DOI: 10.4230/TGDK.4.1.1

On the Computational Cost of Knowledge Graph Embeddings

Authors: Victor Charpenay, Mansour Zoubeirou A Mayaki, and Antoine Zimmermann

Published in: TGDK, Volume 4, Issue 1 (2026). Transactions on Graph Data and Knowledge, Volume 4, Issue 1

Abstract

Over a decade, numerous Knowledge Graph Embedding (KGE) models have been designed and evaluated on reference datasets, always with increasing performance. In this paper, we re-evaluate these models with respect to their computational efficiency during training, by estimating the computational cost of the procedure expressed in floating-point operations. We design a cost model based on analytical expressions and apply it on a collection of 20 KGE models, representative of the state-of-the-art. We show that dimensionality or parameter efficiency, used in the literature to compare models with each other, are not suitable to evaluate the true cost of models. Through fixed-budget experiments, a novel approach to evaluate KGE models based on cost estimates, we re-assess the relative performance of model families compared to the state-of-the-art. Bilinear models such as ComplEx underperform with a low computational budget while hyperbolic linear models appear to offer no particular benefit compared to simpler Euclidian models, especially the MuRE model. Neural models, such as ConvE or CompGCN, achieve reasonable performance in the literature but their high computational cost appears unnecessary when compared with other models. The trade-off between efficiency and expressivity of both linear and neural models is to be further explored.

Cite as

Victor Charpenay, Mansour Zoubeirou A Mayaki, and Antoine Zimmermann. On the Computational Cost of Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 4, Issue 1, pp. 1:1-1:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{charpenay_et_al:TGDK.4.1.1,
  author =	{Charpenay, Victor and Zoubeirou A Mayaki, Mansour and Zimmermann, Antoine},
  title =	{{On the Computational Cost of Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:30},
  ISSN =	{2942-7517},
  year =	{2026},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.4.1.1},
  URN =		{urn:nbn:de:0030-drops-256863},
  doi =		{10.4230/TGDK.4.1.1},
  annote =	{Keywords: Knowledge Graph Embedding, Parameter Efficiency, Computational Budget, Green AI}
}

Document

Survey

DOI: 10.4230/TGDK.3.2.1

Resilience in Knowledge Graph Embeddings

Authors: Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo

Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2

Abstract

In recent years, knowledge graphs have gained interest and witnessed widespread applications in various domains, such as information retrieval, question-answering, recommendation systems, amongst others. Large-scale knowledge graphs to this end have demonstrated their utility in effectively representing structured knowledge. To further facilitate the application of machine learning techniques, knowledge graph embedding models have been developed. Such models can transform entities and relationships within knowledge graphs into vectors. However, these embedding models often face challenges related to noise, missing information, distribution shift, adversarial attacks, etc. This can lead to sub-optimal embeddings and incorrect inferences, thereby negatively impacting downstream applications. While the existing literature has focused so far on adversarial attacks on KGE models, the challenges related to the other critical aspects remain unexplored. In this paper, we, first of all, give a unified definition of resilience, encompassing several factors such as generalisation, in-distribution generalization, distribution adaption, and robustness. After formalizing these concepts for machine learning in general, we define them in the context of knowledge graphs. To find the gap in the existing works on resilience in the context of knowledge graphs, we perform a systematic survey, taking into account all these aspects mentioned previously. Our survey results show that most of the existing works focus on a specific aspect of resilience, namely robustness. After categorizing such works based on their respective aspects of resilience, we discuss the challenges and future research directions.

Cite as

Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo. Resilience in Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 1:1-1:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{sharma_et_al:TGDK.3.2.1,
  author =	{Sharma, Arnab and Kouagou, N'Dah Jean and Ngomo, Axel-Cyrille Ngonga},
  title =	{{Resilience in Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:38},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.1},
  URN =		{urn:nbn:de:0030-drops-248117},
  doi =		{10.4230/TGDK.3.2.1},
  annote =	{Keywords: Knowledge graphs, Resilience, Robustness}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.73

Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians

Authors: François Le Gall

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

We construct classical algorithms computing an approximation of the ground state energy of an arbitrary k-local Hamiltonian acting on n qubits. We first consider the setting where a good "guiding state" is available, which is the main setting where quantum algorithms are expected to achieve an exponential speedup over classical methods. We show that a constant approximation (i.e., an approximation with constant relative accuracy) of the ground state energy can be computed classically in poly (1/χ,n) time and poly(n) space, where χ denotes the overlap between the guiding state and the ground state (as in prior works in dequantization, we assume sample-and-query access to the guiding state). This gives a significant improvement over the recent classical algorithm by Gharibian and Le Gall (SICOMP 2023), and matches (up to a polynomial overhead) both the time and space complexities of quantum algorithms for constant approximation of the ground state energy. We also obtain classical algorithms for higher-precision approximation. For the setting where no guided state is given (i.e., the standard version of the local Hamiltonian problem), we obtain a classical algorithm computing a constant approximation of the ground state energy in 2^O(n) time and poly(n) space. To our knowledge, before this work it was unknown how to classically achieve these bounds simultaneously, even for constant approximation. We also discuss complexity-theoretic aspects of our results.

Cite as

François Le Gall. Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 73:1-73:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{legall:LIPIcs.ESA.2025.73,
  author =	{Le Gall, Fran\c{c}ois},
  title =	{{Classical Algorithms for Constant Approximation of the Ground State Energy of Local Hamiltonians}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{73:1--73:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.73},
  URN =		{urn:nbn:de:0030-drops-245419},
  doi =		{10.4230/LIPIcs.ESA.2025.73},
  annote =	{Keywords: approximation algorithms, quantum computing, dequantization}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.42

(Multivariate) k-SUM as Barrier to Succinct Computation

Authors: Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

How does the time complexity of a problem change when the input is given succinctly rather than explicitly? We study this question for several geometric problems defined on a set X of N points in ℤ^d. As succinct representation, we choose a sumset (or Minkowski sum) representation: Instead of receiving X explicitly, we are given sets A,B of n points that define X as A+B = {a+b∣ a ∈ A,b ∈ B}. We investigate the fine-grained complexity of this succinct version for several Õ(N)-time computable geometric primitives. Remarkably, we can tie their complexity tightly to the complexity of corresponding k-SUM problems. Specifically, we introduce as All-ints 3-SUM(n,n,k) the following multivariate, multi-output variant of 3-SUM: given sets A,B of size n and set C of size k, determine for all c ∈ C whether there are a ∈ A and b ∈ B with a+b = c. We obtain the following results: 1) Succinct closest L_∞-pair requires time N^{1-o(1)} under the 3-SUM hypothesis, while succinct furthest L_∞-pair can be solved in time Õ(n). 2) Succinct bichromatic closest L_∞-Pair requires time N^{1-o(1)} iff the 4-SUM hypothesis holds. 3) The following problems are fine-grained equivalent to All-ints 3-SUM(n,n,k): succinct skyline computation in 2D with output size k and succinct batched orthogonal range search with k given ranges. This establishes conditionally tight Õ(min{nk, N})-time algorithms for these problems. We obtain further connections with All-ints 3-SUM(n,n,k) for succinctly computing independent sets in unit interval graphs. Thus, (Multivariate) k-SUM problems precisely capture the barrier for enabling sumset-succinct computation for various geometric primitives.

Cite as

Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel. (Multivariate) k-SUM as Barrier to Succinct Computation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gokaj_et_al:LIPIcs.ESA.2025.42,
  author =	{Gokaj, Geri and K\"{u}nnemann, Marvin and Storandt, Sabine and Truschel, Carina},
  title =	{{(Multivariate) k-SUM as Barrier to Succinct Computation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{42:1--42:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.42},
  URN =		{urn:nbn:de:0030-drops-245101},
  doi =		{10.4230/LIPIcs.ESA.2025.42},
  annote =	{Keywords: Fine-grained complexity theory, sumsets, additive combinatorics, succinct inputs, computational geometry}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.23

On the Instance Optimality of Detecting Collisions and Subgraphs

Authors: Omri Ben-Eliezer, Tomer Grossman, and Moni Naor

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

Suppose you are given a function f: [n] → [n] via (black-box) query access to the function. You are looking to find something local, like a collision (a pair x ≠ y s.t. f(x) = f(y)). The question is whether knowing the "shape" of the function helps you or not (by shape we mean that some permutation of the function is known). Formally, we investigate the unlabeled instance optimality of substructure detection problems in graphs and functions. A problem is g(n)-instance optimal if it admits an algorithm A satisfying that for any possible input, the (randomized) query complexity of A is at most g(n) times larger than the query complexity of any algorithm A' which solves the same problem while holding an unlabeled copy of the input (i.e., any A' that "knows the structure of the input"). Our results point to a trichotomy of unlabeled instance optimality among substructure detection problems in graphs and functions: - A few very simple properties have an O(1)-instance optimal algorithm. - Most properties of graphs and functions, with examples such as containing a fixed point or a 3-collision in functions, or a triangle in graphs, are n^{c}-far from instance optimal for some constant c > 0. - The problems of collision detection in functions and finding a claw in a graph serve as a middle ground between the two regimes. We show that these two properties are not Ω(log n)-instance optimal, and conjecture that this bound is tight. We provide evidence towards this conjecture, by proving that finding a claw in a graph is O(log(n))-instance optimal among all input graphs for which the query complexity of an algorithm holding an unlabeled certificate is O(√{n/(log n)}).

Cite as

Omri Ben-Eliezer, Tomer Grossman, and Moni Naor. On the Instance Optimality of Detecting Collisions and Subgraphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2025.23,
  author =	{Ben-Eliezer, Omri and Grossman, Tomer and Naor, Moni},
  title =	{{On the Instance Optimality of Detecting Collisions and Subgraphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.23},
  URN =		{urn:nbn:de:0030-drops-234002},
  doi =		{10.4230/LIPIcs.ICALP.2025.23},
  annote =	{Keywords: instance optimality, instance complexity, unlabeled certificate, subgraph detection, collision detection}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.113

Nearly Optimal Circuit Size for Sparse Quantum State Preparation

Authors: Lvzhou Li and Jingquan Luo

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

Quantum state preparation is a fundamental and significant subroutine in quantum computing. In this paper, we conduct a systematic investigation of the circuit size (the total count of elementary gates in the circuit) for sparse quantum state preparation. A quantum state is said to be d-sparse if it has only d non-zero amplitudes. For the task of preparing an n-qubit d-sparse quantum state, we obtain the following results: - Without ancillary qubits: Any n-qubit d-sparse quantum state can be prepared by a quantum circuit of size O(nd/(log n) + n) without using ancillary qubits, which improves the previous best results. It is asymptotically optimal when d = poly(n), and this optimality holds for a broader scope under some reasonable assumptions. - With limited ancillary qubits: (i) Based on the first result, we prove for the first time a trade-off between the number of ancillary qubits and the circuit size: any n-qubit d-sparse quantum state can be prepared by a quantum circuit of size O((nd)/(log(n + m)) + n) using m ancillary qubits for any m ∈ O((nd)/(log nd) + n). (ii) We establish a matching lower bound Ω((nd)/(log(n+m))+n) under some reasonable assumptions, and obtain a slightly weaker lower bound Ω((nd)/(log(n+m)+log d) + n) without any assumptions. - With unlimited ancillary qubits: Given an arbitrary amount of ancillary qubits available, the circuit size for preparing n-qubit d-sparse quantum states is Θ((nd)/(log nd) + n).

Cite as

Lvzhou Li and Jingquan Luo. Nearly Optimal Circuit Size for Sparse Quantum State Preparation. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 113:1-113:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.ICALP.2025.113,
  author =	{Li, Lvzhou and Luo, Jingquan},
  title =	{{Nearly Optimal Circuit Size for Sparse Quantum State Preparation}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{113:1--113:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.113},
  URN =		{urn:nbn:de:0030-drops-234900},
  doi =		{10.4230/LIPIcs.ICALP.2025.113},
  annote =	{Keywords: Quantum computing, quantum state preparation, circuit complexity}
}

Document

DOI: 10.4230/LIPIcs.STACS.2025.74

Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay

Authors: Noam Touitou

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract

We consider the online service with delay problem, in which a server traverses a metric space to serve requests that arrive over time. Requests gather individual delay cost while awaiting service, penalizing service latency; an algorithm seeks to minimize both its movement cost and the total delay cost. Algorithms for the problem (on general metric spaces) are only known for the clairvoyant model, where the algorithm knows future delay cost in advance (e.g., Azar et al., STOC'17; Azar and Touitou, FOCS'19; Touitou, STOC'23). However, in the non-clairvoyant setting, only negative results are known: where n is the size of the metric space and m is the number of requests, there are lower bounds of Ω(√n) and Ω(√m) on competitiveness (Azar et al., STOC'17), that hold even for randomized algorithms (Le et al., SODA'23). In this paper, we present the first algorithm for non-clairvoyant online service with delay. Our algorithm is deterministic and O(min{√n log n, √m log m})-competitive; combined with the lower bounds of Azar et al., this settles the correct competitive ratio for the problem up to logarithmic factors, in terms of both n and m.

Cite as

Noam Touitou. Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 74:1-74:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{touitou:LIPIcs.STACS.2025.74,
  author =	{Touitou, Noam},
  title =	{{Nearly-Optimal Algorithm for Non-Clairvoyant Service with Delay}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{74:1--74:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.74},
  URN =		{urn:nbn:de:0030-drops-228995},
  doi =		{10.4230/LIPIcs.STACS.2025.74},
  annote =	{Keywords: Online, Delay, Deadlines, k-server, Non-clairvoyant}
}

Document

DOI: 10.4230/LIPIcs.STACS.2025.59

Online Matching with Delays and Size-Based Costs

Authors: Yasushi Kawase and Tomohiro Nakayoshi

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract

In this paper, we introduce the problem of Online Matching with Delays and Size-based Costs (OMDSC). The OMDSC problem involves m requests arriving online. At any time, a group can be formed by matching any number of requests that have been received but remain unmatched. The cost associated with each group is determined by the waiting time for each request within the group and size-dependent cost. The size-dependent cost is specified by a penalty function. Our goal is to partition all the incoming requests into multiple groups while minimizing the total associated cost. This problem is an extension of the TCP acknowledgment problem proposed by Dooly et al. (J. ACM, 2001). It generalizes the cost model for sending acknowledgments. This study reveals the competitive ratios for a fundamental case, in which the penalty function takes only values of either 0 or 1. We classify such penalty functions into three distinct cases: (i) a fixed penalty of 1 regardless of the group size, (ii) a penalty of 0 if and only if the group size is a multiple of a specific integer k, and (iii) other situations. The problem in case (i) is equivalent to the TCP acknowledgment problem, for which Dooly et al. proposed a 2-competitive algorithm. For case (ii), we first show that natural algorithms that match all remaining requests are Ω(√k)-competitive. We then propose an O(log k / log log k)-competitive deterministic algorithm by carefully managing the match size and timing, and prove its optimality. For any penalty function in case (iii), we demonstrate the non-existence of a competitive online algorithm. Additionally, we discuss competitive ratios for other typical penalty functions that are not restricted to take values of 0 or 1.

Cite as

Yasushi Kawase and Tomohiro Nakayoshi. Online Matching with Delays and Size-Based Costs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kawase_et_al:LIPIcs.STACS.2025.59,
  author =	{Kawase, Yasushi and Nakayoshi, Tomohiro},
  title =	{{Online Matching with Delays and Size-Based Costs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{59:1--59:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.59},
  URN =		{urn:nbn:de:0030-drops-228846},
  doi =		{10.4230/LIPIcs.STACS.2025.59},
  annote =	{Keywords: Online matching, competitive analysis, delayed service}
}

Document

Position

DOI: 10.4230/TGDK.1.1.5

Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities

Authors: Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract

The term life sciences refers to the disciplines that study living organisms and life processes, and include chemistry, biology, medicine, and a range of other related disciplines. Research efforts in life sciences are heavily data-driven, as they produce and consume vast amounts of scientific data, much of which is intrinsically relational and graph-structured. The volume of data and the complexity of scientific concepts and relations referred to therein promote the application of advanced knowledge-driven technologies for managing and interpreting data, with the ultimate aim to advance scientific discovery. In this survey and position paper, we discuss recent developments and advances in the use of graph-based technologies in life sciences and set out a vision for how these technologies will impact these fields into the future. We focus on three broad topics: the construction and management of Knowledge Graphs (KGs), the use of KGs and associated technologies in the discovery of new knowledge, and the use of KGs in artificial intelligence applications to support explanations (explainable AI). We select a few exemplary use cases for each topic, discuss the challenges and open research questions within these topics, and conclude with a perspective and outlook that summarizes the overarching challenges and their potential solutions as a guide for future research.

Cite as

Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma. Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 5:1-5:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{chen_et_al:TGDK.1.1.5,
  author =	{Chen, Jiaoyan and Dong, Hang and Hastings, Janna and Jim\'{e}nez-Ruiz, Ernesto and L\'{o}pez, Vanessa and Monnin, Pierre and Pesquita, Catia and \v{S}koda, Petr and Tamma, Valentina},
  title =	{{Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:33},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.5},
  URN =		{urn:nbn:de:0030-drops-194791},
  doi =		{10.4230/TGDK.1.1.5},
  annote =	{Keywords: Knowledge graphs, Life science, Knowledge discovery, Explainable AI}
}

Document

Position

DOI: 10.4230/TGDK.1.1.2

Large Language Models and Knowledge Graphs: Opportunities and Challenges

Authors: Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract

Large Language Models (LLMs) have taken Knowledge Representation - and the world - by storm. This inflection point marks a shift from explicit knowledge representation to a renewed focus on the hybrid representation of both explicit knowledge and parametric knowledge. In this position paper, we will discuss some of the common debate points within the community on LLMs (parametric knowledge) and Knowledge Graphs (explicit knowledge) and speculate on opportunities and visions that the renewed focus brings, as well as related research topics and challenges.

Cite as

Jeff Z. Pan, Simon Razniewski, Jan-Christoph Kalo, Sneha Singhania, Jiaoyan Chen, Stefan Dietze, Hajira Jabeen, Janna Omeliyanenko, Wen Zhang, Matteo Lissandrini, Russa Biswas, Gerard de Melo, Angela Bonifati, Edlira Vakaj, Mauro Dragoni, and Damien Graux. Large Language Models and Knowledge Graphs: Opportunities and Challenges. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 2:1-2:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{pan_et_al:TGDK.1.1.2,
  author =	{Pan, Jeff Z. and Razniewski, Simon and Kalo, Jan-Christoph and Singhania, Sneha and Chen, Jiaoyan and Dietze, Stefan and Jabeen, Hajira and Omeliyanenko, Janna and Zhang, Wen and Lissandrini, Matteo and Biswas, Russa and de Melo, Gerard and Bonifati, Angela and Vakaj, Edlira and Dragoni, Mauro and Graux, Damien},
  title =	{{Large Language Models and Knowledge Graphs: Opportunities and Challenges}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:38},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.2},
  URN =		{urn:nbn:de:0030-drops-194766},
  doi =		{10.4230/TGDK.1.1.2},
  annote =	{Keywords: Large Language Models, Pre-trained Language Models, Knowledge Graphs, Ontology, Retrieval Augmented Language Models}
}

Document

Survey

DOI: 10.4230/TGDK.1.1.11

How Does Knowledge Evolve in Open Knowledge Graphs?

Authors: Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract

Openly available, collaboratively edited Knowledge Graphs (KGs) are key platforms for the collective management of evolving knowledge. The present work aims t o provide an analysis of the obstacles related to investigating and processing specifically this central aspect of evolution in KGs. To this end, we discuss (i) the dimensions of evolution in KGs, (ii) the observability of evolution in existing, open, collaboratively constructed Knowledge Graphs over time, and (iii) possible metrics to analyse this evolution. We provide an overview of relevant state-of-the-art research, ranging from metrics developed for Knowledge Graphs specifically to potential methods from related fields such as network science. Additionally, we discuss technical approaches - and their current limitations - related to storing, analysing and processing large and evolving KGs in terms of handling typical KG downstream tasks.

Cite as

Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs. How Does Knowledge Evolve in Open Knowledge Graphs?. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 11:1-11:59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{polleres_et_al:TGDK.1.1.11,
  author =	{Polleres, Axel and Pernisch, Romana and Bonifati, Angela and Dell'Aglio, Daniele and Dobriy, Daniil and Dumbrava, Stefania and Etcheverry, Lorena and Ferranti, Nicolas and Hose, Katja and Jim\'{e}nez-Ruiz, Ernesto and Lissandrini, Matteo and Scherp, Ansgar and Tommasini, Riccardo and Wachs, Johannes},
  title =	{{How Does Knowledge Evolve in Open Knowledge Graphs?}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{11:1--11:59},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.11},
  URN =		{urn:nbn:de:0030-drops-194855},
  doi =		{10.4230/TGDK.1.1.11},
  annote =	{Keywords: KG evolution, temporal KG, versioned KG, dynamic KG}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2017.20

An Efficient Fixed-Parameter Algorithm for the 2-Plex Bipartition Problem

Authors: Li-Hsuan Chen, Sun-Yuan Hsieh, Ling-Ju Hung, and Peter Rossmanith

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract

Given a graph G=(V, E), an s-plex S\subseteq V is a vertex subset such that for v\in S the degree of v in G[S] is at least |S|-s. An s-plex bipartition \mathcal{P}=(V_1, V_2) is a bipartition of G=(V, E), V=V_1\uplus V_2, satisfying that both V_1 and V_2 are s-plexes. Given an instance G=(V, E) and a parameter k, the s-Plex Bipartition problem asks whether there exists an s-plex bipartition of G such that min{|V_1|, |V_2|\}\leq k. The s-Plex Bipartition problem is NP-complete. However, it is still open whether this problem is fixed-parameter tractable. In this paper, we give a fixed-parameter algorithm for 2-Plex Bipartition running in time O*(2.4143^k). A graph G = (V, E) is called defective (p, d)-colorable if it admits a vertex coloring with p colors such that each color class in G induces a subgraph of maximum degree at most d. A graph G admits an s-plex bipartition if and only if the complement graph of G, \bar{G}, admits a defective (2, s-1)-coloring such that one of the two color classes is of size at most k. By applying our fixed-parameter algorithm as a subroutine, one can find a defective (2,1)-coloring with one of the two colors of minimum cardinality for a given graph in O*(1.5539^n) time where n is the number of vertices in the input graph.

Cite as

Li-Hsuan Chen, Sun-Yuan Hsieh, Ling-Ju Hung, and Peter Rossmanith. An Efficient Fixed-Parameter Algorithm for the 2-Plex Bipartition Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2017.20,
  author =	{Chen, Li-Hsuan and Hsieh, Sun-Yuan and Hung, Ling-Ju and Rossmanith, Peter},
  title =	{{An Efficient Fixed-Parameter Algorithm for the 2-Plex Bipartition Problem}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.20},
  URN =		{urn:nbn:de:0030-drops-82458},
  doi =		{10.4230/LIPIcs.ISAAC.2017.20},
  annote =	{Keywords: 2-plex, 2-plex bipartition, bounded-degree-1 set bipartition, defective (2,1)-coloring}
}

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