26 Search Results for "Klein, Kim-Manuel"

Document
Invited Talk
DOI: 10.4230/LIPIcs.IPEC.2025.1
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)

Authors: Martin Koutecký

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
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Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
  author =	{Kouteck\'{y}, Martin},
  title =	{{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
  URN =		{urn:nbn:de:0030-drops-251338},
  doi =		{10.4230/LIPIcs.IPEC.2025.1},
  annote =	{Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
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Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.14
A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma

Authors: Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman, and Meirav Zehavi

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We present an algorithm for a class of n-fold ILPs whose existing algorithms in literature are often either (1) based on the augmentation framework where one starts with an arbitrary solution and then iteratively moves towards an optimal solution by solving appropriate programs; or (2) require solving a linear relaxation of the program; or (3) are based on decomposition/proximity based arguments. Combinatorial n-fold ILPs is a class of n-fold ILPs introduced and studied by Knop et al. [MP2020] that captures several other problems in a variety of domains. We present a simple and direct algorithm that solves combinatorial n-fold ILPs with unbounded non-negative variables via an application of the Steinitz lemma. Depending on the structure of the input ILP, we also improve upon the existing algorithms in the literature in terms of the running time, thereby showing an improvement that mirrors the one shown by Rohwedder [ICALP2025] contemporaneously and independently.
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Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman, and Meirav Zehavi. A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gupta_et_al:LIPIcs.IPEC.2025.14,
  author =	{Gupta, Sushmita and Jain, Pallavi and Seetharaman, Sanjay and Zehavi, Meirav},
  title =	{{A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.14},
  URN =		{urn:nbn:de:0030-drops-251467},
  doi =		{10.4230/LIPIcs.IPEC.2025.14},
  annote =	{Keywords: n-fold integer linear program, parameterized algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.15
New Algorithm for Combinatorial n-Folds and Applications

Authors: Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address n-fold ILPs where the matrix 𝒜 has a specific structure, i.e., where the blocks in the lower part of 𝒜 consist only of the row vectors (1,… ,1). In this paper, we propose an approach tailored to exactly these combinatorial n-folds. We utilize a divide and conquer approach to separate the original problem such that the right-hand side iteratively decreases in size. We show that this decrease in size can be calculated such that we only need to consider a bounded amount of possible right-hand sides. This, in turn, lets us efficiently combine solutions of the smaller right-hand sides to solve the original problem. We can decide the feasibility of, and also optimally solve, such problems in time (n r Δ)^O(r) log(‖b‖_∞), where n is the number of blocks, r the number of rows in the upper blocks and Δ = ‖A‖_∞. We complement the algorithm by discussing applications of the n-fold ILPs with the specific structure we require. We consider the problems of (i) scheduling on uniform machines, (ii) closest string and (iii) (graph) imbalance. Regarding (i), our algorithm results in running times of p_max^O(d)|I|^O(1), matching a lower bound derived via ETH. For (ii) we achieve running times matching the current state-of-the-art in the general case. In contrast to the state-of-the-art, our result can leverage a bounded number of column-types to yield an improved running time. For (iii), we improve the parameter dependency on the size of the vertex cover.
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Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas. New Algorithm for Combinatorial n-Folds and Applications. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.15,
  author =	{Jansen, Klaus and Kahler, Kai and Pirotton, Lis and Tutas, Malte},
  title =	{{New Algorithm for Combinatorial n-Folds and Applications}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.15},
  URN =		{urn:nbn:de:0030-drops-251472},
  doi =		{10.4230/LIPIcs.IPEC.2025.15},
  annote =	{Keywords: integer linear programming, n-fold, parameterized complexity, scheduling, uniform machines}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.15
Parameterized Complexity of Directed Traveling Salesman Problem

Authors: Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý

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

Abstract
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed walk of minimum length (or total weight) that visits every vertex of the given graph at least once. In a yet more general version, Directed Waypoint Routing Problem (DWRP), some vertices are marked as terminals and we are only required to visit all terminals. Furthermore, each edge has its capacity bounding the number of times this edge can be used by a solution. While both problems (and many other variants of TSP) were extensively investigated, mostly from the approximation point of view, there are surprisingly few results concerning the parameterized complexity. Our starting point is the result of Marx et al. [APPROX/RANDOM 2016] who proved that DTSP is W[1]-hard parameterized by distance to pathwidth 3. In this paper we aim to initiate the systematic complexity study of variants of Directed Traveling Salesman Problem with respect to various, mostly structural, parameters. We show that DWRP is FPT parameterized by the solution size, the feedback edge number and the vertex integrity of the underlying undirected graph. Furthermore, the problem is XP parameterized by treewidth. On the complexity side, we show that the problem is W[1]-hard parameterized by the distance to constant treedepth.
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Václav Blažej, Andreas Emil Feldmann, Foivos Fioravantes, Paweł Rzążewski, and Ondřej Suchý. Parameterized Complexity of Directed Traveling Salesman Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blazej_et_al:LIPIcs.ISAAC.2025.15,
  author =	{Bla\v{z}ej, V\'{a}clav and Feldmann, Andreas Emil and Fioravantes, Foivos and Rz\k{a}\.{z}ewski, Pawe{\l} and Such\'{y}, Ond\v{r}ej},
  title =	{{Parameterized Complexity of Directed Traveling Salesman Problem}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.15},
  URN =		{urn:nbn:de:0030-drops-249231},
  doi =		{10.4230/LIPIcs.ISAAC.2025.15},
  annote =	{Keywords: Directed TSP, parameterized complexity, vertex integrity, treedepth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.48
The Support of Bin Packing Is Exponential

Authors: Klaus Jansen, Lis Pirotton, and Malte Tutas

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

Abstract
Consider the classical Bin Packing problem with d different item sizes s_i and amounts of items a_i. The support of a Bin Packing solution is the number of differently filled bins. In this work, we show that the lower bound on the support of this problem is 2^Ω(d). Our lower bound matches the upper bound of 2^d given by Eisenbrand and Shmonin [Oper.Research Letters '06] up to a constant factor. This result has direct implications for the time complexity of several Bin Packing algorithms, such as Goemans and Rothvoss [SODA '14], Jansen and Klein [SODA '17] and Jansen and Solis-Oba [IPCO '10]. To achieve our main result, we develop a technique to aggregate equality constrained ILPs with many constraints into an equivalent ILP with one constraint. Our technique contrasts existing aggregation techniques as we manage to integrate upper bounds on variables into the resulting constraint. We believe this technique can be useful for solving general ILPs or the d-dimensional knapsack problem.
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Klaus Jansen, Lis Pirotton, and Malte Tutas. The Support of Bin Packing Is Exponential. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.ESA.2025.48,
  author =	{Jansen, Klaus and Pirotton, Lis and Tutas, Malte},
  title =	{{The Support of Bin Packing Is Exponential}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{48:1--48:16},
  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.2025.48},
  URN =		{urn:nbn:de:0030-drops-245167},
  doi =		{10.4230/LIPIcs.ESA.2025.48},
  annote =	{Keywords: Bin Packing, Integer Programming, Support}
}
Document
DOI: 10.4230/OASIcs.Programming.2025.23
The Pyttern Program Query Language

Authors: Julien Liénard, Kim Mens, and Siegfried Nijssen

Published in: OASIcs, Volume 134, Companion Proceedings of the 9th International Conference on the Art, Science, and Engineering of Programming (Programming 2025)

Abstract
Despite the availability of numerous tools and languages for detecting structural patterns in programs, their complexity often presents a steep learning curve. This highlights the need for a program query language that is easier to learn, use, and read while remaining sufficiently expressive for defining and detecting relevant structural coding patterns in program code. To address this challenge, we present Pyttern, a query language that extends Python syntax with regular-expression-inspired wildcards, enabling intuitive pattern-based querying of Python code. Its implementation relies upon a custom pushdown automaton describing how to match patterns over program parse trees, thus providing a robust foundation for structural code analysis. We evaluate Pyttern’s usability and effectiveness through a study involving 35 master’s students, who were asked to write seven different patterns to identify known programming misconceptions. The results demonstrate that Pyttern is both easy to learn and practical to use, at least for analysing small-scale programs.
Cite as

Julien Liénard, Kim Mens, and Siegfried Nijssen. The Pyttern Program Query Language. In Companion Proceedings of the 9th International Conference on the Art, Science, and Engineering of Programming (Programming 2025). Open Access Series in Informatics (OASIcs), Volume 134, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lienard_et_al:OASIcs.Programming.2025.23,
  author =	{Li\'{e}nard, Julien and Mens, Kim and Nijssen, Siegfried},
  title =	{{The Pyttern Program Query Language}},
  booktitle =	{Companion Proceedings of the 9th International Conference on the Art, Science, and Engineering of Programming (Programming 2025)},
  pages =	{23:1--23:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-382-9},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{134},
  editor =	{Edwards, Jonathan and Perera, Roly and Petricek, Tomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Programming.2025.23},
  URN =		{urn:nbn:de:0030-drops-243075},
  doi =		{10.4230/OASIcs.Programming.2025.23},
  annote =	{Keywords: Pyttern, Program Query Languages, Python, Pattern Matching, Parse Tree, Pushdown Automaton, Static Code Analysis, Wildcards, Tree Pattern Matching}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.25
An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines

Authors: Leah Epstein and Asaf Levin

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study a classic scheduling problem on uniformly related machines for which we show an efficient polynomial time approximation scheme (EPTAS), where an EPTAS is a fast and practical approximation scheme. For a desired approximation ratio of 1+ε for ε > 0, the running time of an EPTAS is a function of ε multiplied by a polynomial function of the input length. New methods and techniques are essential in developing such improved approximation schemes, and their design is a primary goal of this research agenda. We present an EPTAS for the scheduling problem of a set of jobs on uniformly related machines so as to minimize the total weighted completion time. The problem is NP-hard in the strong sense, and therefore an EPTAS is the best possible approximation scheme for the problem, unless P=NP. Prior to our work, only a PTAS was known for the problem, while an EPTAS was known only for the special case of identical machines.
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Leah Epstein and Asaf Levin. An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 25:1-25:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epstein_et_al:LIPIcs.WADS.2025.25,
  author =	{Epstein, Leah and Levin, Asaf},
  title =	{{An Efficient Polynomial Time Approximation Scheme for Minimizing the Total Weighted Completion Time on Uniformly Related Machines}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{25:1--25:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.25},
  URN =		{urn:nbn:de:0030-drops-242564},
  doi =		{10.4230/LIPIcs.WADS.2025.25},
  annote =	{Keywords: Scheduling algorithms, Approximation schemes, Min-sum objective}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.112
Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns

Authors: Alexandra Lassota and Koen Ligthart

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

Abstract
We study integer linear programs (ILP) of the form min{c^⊤ x | Ax = b,l ≤ x ≤ u,x ∈ ℤⁿ} and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the well-established approach of capturing the hardness of a problem by the distance to triviality. The generalized matching problem is an ILP where each column of the constraint matrix has 1-norm of at most 2. It captures several well-known polynomial time solvable problems such as matching and flow problems. We parameterize by the size of variable and constraint backdoors, which measure the least number of columns or rows that must be deleted to obtain a generalized matching ILP. This extends generalized matching problems by allowing a parameterized number of additional arbitrary variables or constraints, yielding a novel parameter. We present the following results: (i) a fixed-parameter tractable (FPT) algorithm for ILPs parameterized by the size p of a minimum variable backdoor to generalized matching; (ii) a randomized slice-wise polynomial (XP) time algorithm for ILPs parameterized by the size h of a minimum constraint backdoor to generalized matching as long as c and A are encoded in unary; (iii) we complement (ii) by proving that solving an ILP is W[1]-hard when parameterized by h even when c,A,l,u have coefficients of constant size. To obtain (i), we prove a variant of lattice-convexity of the degree sequences of weighted b-matchings, which we study in the light of SBO jump M-convex functions. This allows us to model the matching part as a polyhedral constraint on the integer backdoor variables. The resulting ILP is solved in FPT time using an integer programming algorithm. For (ii), the randomized XP time algorithm is obtained by pseudo-polynomially reducing the problem to the exact matching problem. To prevent an exponential blowup in terms of the encoding length of b, we bound the Graver complexity of the constraint matrix and employ a Graver augmentation local search framework. The hardness result (iii) is obtained through a parameterized reduction from ILP with h constraints and coefficients encoded in unary.
Cite as

Alexandra Lassota and Koen Ligthart. Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 112:1-112:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lassota_et_al:LIPIcs.ICALP.2025.112,
  author =	{Lassota, Alexandra and Ligthart, Koen},
  title =	{{Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{112:1--112:18},
  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.2025.112},
  URN =		{urn:nbn:de:0030-drops-234895},
  doi =		{10.4230/LIPIcs.ICALP.2025.112},
  annote =	{Keywords: Integer Programming, fixed-parameter Tractability, polyhedral Optimization, Matchings}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.127
Cost Preserving Dependent Rounding for Allocation Problems

Authors: Lars Rohwedder, Arman Rouhani, and Leo Wennmann

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

Abstract
We present a dependent randomized rounding scheme, which rounds fractional solutions to integral solutions satisfying certain hard constraints on the output while preserving Chernoff-like concentration properties. In contrast to previous dependent rounding schemes, our algorithm guarantees that the cost of the rounded integral solution does not exceed that of the fractional solution. Our algorithm works for a class of assignment problems with restrictions similar to those of prior works. In a non-trivial combination of our general result with a classical approach from Shmoys and Tardos [Math. Programm.'93] and more recent linear programming techniques developed for the restricted assignment variant by Bansal, Sviridenko [STOC'06] and Davies, Rothvoss, Zhang [SODA'20], we derive a O(log n)-approximation algorithm for the Budgeted Santa Claus Problem. In this new variant, the goal is to allocate resources with different values to players, maximizing the minimum value a player receives, and satisfying a budget constraint on player-resource allocation costs.
Cite as

Lars Rohwedder, Arman Rouhani, and Leo Wennmann. Cost Preserving Dependent Rounding for Allocation Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder_et_al:LIPIcs.ICALP.2025.127,
  author =	{Rohwedder, Lars and Rouhani, Arman and Wennmann, Leo},
  title =	{{Cost Preserving Dependent Rounding for Allocation Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{127:1--127:20},
  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.2025.127},
  URN =		{urn:nbn:de:0030-drops-235049},
  doi =		{10.4230/LIPIcs.ICALP.2025.127},
  annote =	{Keywords: Matching, Randomized Rounding, Santa Claus, Approximation Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.126
ETH-Tight FPT Algorithm for Makespan Minimization on Uniform Machines

Authors: Lars Rohwedder

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

Abstract
Given n jobs with processing times p₁,...,p_n ∈ ℕ and m ≤ n machines with speeds s₁,...,s_m ∈ ℕ our goal is to allocate the jobs to machines minimizing the makespan. We present an algorithm that solves the problem in time p_{max}^{O(d)} ⋅ n, where p_{max} is the maximum processing time and d ≤ p_{max} is the number of distinct processing times. This is essentially the best possible due to a lower bound based on the exponential time hypothesis (ETH). Our result improves over prior works that had a quadratic term in d in the exponent and answers an open question by Koutecký and Zink. The algorithm is based on integer programming techniques combined with novel ideas from modular arithmetic. It can also be implemented efficiently for the more compact high-multiplicity instance encoding.
Cite as

Lars Rohwedder. ETH-Tight FPT Algorithm for Makespan Minimization on Uniform Machines. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 126:1-126:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder:LIPIcs.ICALP.2025.126,
  author =	{Rohwedder, Lars},
  title =	{{ETH-Tight FPT Algorithm for Makespan Minimization on Uniform Machines}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{126:1--126:13},
  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.2025.126},
  URN =		{urn:nbn:de:0030-drops-235037},
  doi =		{10.4230/LIPIcs.ICALP.2025.126},
  annote =	{Keywords: Scheduling, Integer Programming}
}
Document
DOI: 10.4230/OASIcs.NG-RES.2025.2
Low-Latency Real-Time Applications on Heterogeneous MPSoCs

Authors: Nicolas Coppik, Pascal Becker, and Marcus Ritter

Published in: OASIcs, Volume 128, Sixth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2025)

Abstract
Heterogeneous Multi-Processor Systems-on-Chip (MPSoCs) that combine multiple, heterogeneous processing units are becoming increasingly popular for a wide range of applications, including industrial applications, where complex real-time applications can benefit from the performance and flexibility they offer. However, deploying real-time applications with low latency requirements across multiple processing units on such MPSoCs remains a challenging problem, particularly when communication between processors is required on a time-critical path. Existing solutions generally rely on the presence of at least one full-featured, general-purpose operating system on the device, and do not cater to the requirements of distributed, low-latency real-time applications. In this paper, we investigate the performance, with a focus on latency, of different options for communication between CPUs, including inter-processor interrupts and shared memory communication via different memories, on the popular Xilinx Zynq UltraScale+ platform and propose a novel solution for communication between heterogeneous processing units that relies only on the availability of shared memory. Our solution is capable of achieving sub-microsecond latencies for signaling and the transfer of small amounts of data between processing units, making it suitable for deploying distributed, low-latency real-time applications.
Cite as

Nicolas Coppik, Pascal Becker, and Marcus Ritter. Low-Latency Real-Time Applications on Heterogeneous MPSoCs. In Sixth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2025). Open Access Series in Informatics (OASIcs), Volume 128, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{coppik_et_al:OASIcs.NG-RES.2025.2,
  author =	{Coppik, Nicolas and Becker, Pascal and Ritter, Marcus},
  title =	{{Low-Latency Real-Time Applications on Heterogeneous MPSoCs}},
  booktitle =	{Sixth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2025)},
  pages =	{2:1--2:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-366-9},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{128},
  editor =	{Yomsi, Patrick Meumeu and Wildermann, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NG-RES.2025.2},
  URN =		{urn:nbn:de:0030-drops-229883},
  doi =		{10.4230/OASIcs.NG-RES.2025.2},
  annote =	{Keywords: real-time systems, heterogeneous systems, latency, inter-core communication}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.47
Minimizing the Number of Tardy Jobs with Uniform Processing Times on Parallel Machines

Authors: Klaus Heeger and Hendrik Molter

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

Abstract
In this work, we study the computational (parameterized) complexity of P∣ r_j, p_j = p ∣∑ w_j U_j. Here, we are given m identical parallel machines and n jobs with equal processing time, each characterized by a release date, a due date, and a weight. The task is to find a feasible schedule, that is, an assignment of the jobs to starting times on machines, such that no job starts before its release date and no machine processes several jobs at the same time, that minimizes the weighted number of tardy jobs. A job is considered tardy if it finishes after its due date. Our main contribution is showing that P∣r_j, p_j = p∣∑ U_j (the unweighted version of the problem) is NP-hard and W[2]-hard when parameterized by the number of machines. The former resolves an open problem in Note 2.1.19 by Kravchenko and Werner [Journal of Scheduling, 2011] and Open Problem 2 by Sgall [ESA, 2012], and the latter resolves Open Problem 7 by Mnich and van Bevern [Computers & Operations Research, 2018]. Furthermore, our result shows that the known XP-algorithm by Baptiste et al. [4OR, 2004] for P∣r_j, p_j = p∣∑ w_j U_j parameterized by the number of machines is optimal from a classification standpoint. On the algorithmic side, we provide alternative running time bounds for the above-mentioned known XP-algorithm. Our analysis shows that P∣r_j, p_j = p∣∑ w_j U_j is contained in XP when parameterized by the processing time, and that it is contained in FPT when parameterized by the combination of the number of machines and the processing time. Finally, we give an FPT-algorithm for P∣r_j, p_j = p∣∑ w_j U_j parameterized by the number of release dates or the number of due dates. With this work, we lay out the foundation for a systematic study of the parameterized complexity of P∣r_j, p_j = p∣∑ w_j U_j.
Cite as

Klaus Heeger and Hendrik Molter. Minimizing the Number of Tardy Jobs with Uniform Processing Times on Parallel Machines. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{heeger_et_al:LIPIcs.STACS.2025.47,
  author =	{Heeger, Klaus and Molter, Hendrik},
  title =	{{Minimizing the Number of Tardy Jobs with Uniform Processing Times on Parallel Machines}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{47:1--47:17},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-228736},
  doi =		{10.4230/LIPIcs.STACS.2025.47},
  annote =	{Keywords: Scheduling, Identical Parallel Machines, Weighted Number of Tardy Jobs, Uniform Processing Times, Release Dates, NP-hard Problems, Parameterized Complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.36
MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal

Authors: Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma

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

Abstract
In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal st-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In the Maximum Minimal st-Separator problem, given a graph G, two distinct vertices s and t and a positive integer k, the goal is to determine whether there exists a minimal st-separator in G of size at least k. Similarly, the Maximum Minimal OCT problem seeks to determine if there exists a minimal set of vertices whose deletion results in a bipartite graph, and whose size is at least k. We demonstrate that both problems are fixed-parameter tractable parameterized by k. Our FPT algorithm for Maximum Minimal st-Separator answers the open question by Hanaka, Bodlaender, van der Zanden & Ono [TCS 2019]. One unique insight from this work is the following. We use the meta-result of Lokshtanov, Ramanujan, Saurabh & Zehavi [ICALP 2018] that enables us to reduce our problems to highly unbreakable graphs. This is interesting, as an explicit use of the recursive understanding and randomized contractions framework of Chitnis, Cygan, Hajiaghayi, Pilipczuk & Pilipczuk [SICOMP 2016] to reduce to the highly unbreakable graphs setting (which is the result that Lokshtanov et al. tries to abstract out in their meta-theorem) does not seem obvious because certain "extension" variants of our problems are W[1]-hard.
Cite as

Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma. MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gaikwad_et_al:LIPIcs.STACS.2025.36,
  author =	{Gaikwad, Ajinkya and Kumar, Hitendra and Maity, Soumen and Saurabh, Saket and Sharma, Roohani},
  title =	{{MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{36:1--36:21},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-228622},
  doi =		{10.4230/LIPIcs.STACS.2025.36},
  annote =	{Keywords: Parameterized Complexity, FPT, MaxMin problems, Maximum Minimal st-separator, Maximum Minimal Odd Cycle Transversal, Unbreakable Graphs, CMSO, Long Induced Odd Cycles, Sunflower Lemma}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.25
Local Density and Its Distributed Approximation

Authors: Aleksander Bjørn Christiansen, Ivor van der Hoog, and Eva Rotenberg

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

Abstract
The densest subgraph problem is a classic problem in combinatorial optimisation. Graphs with low maximum subgraph density are often called "uniformly sparse", leading to algorithms parameterised by this density. However, in reality, the sparsity of a graph is not necessarily uniform. This calls for a formally well-defined, fine-grained notion of density. Danisch, Chan, and Sozio propose a definition for local density that assigns to each vertex v a value ρ^*(v). This local density is a generalisation of the maximum subgraph density of a graph. I.e., if ρ(G) is the subgraph density of a finite graph G, then ρ(G) equals the maximum local density ρ^*(v) over vertices v in G. They present a Frank-Wolfe-based algorithm to approximate the local density of each vertex with no theoretical (asymptotic) guarantees. We provide an extensive study of this local density measure. Just as with (global) maximum subgraph density, we show that there is a dual relation between the local out-degrees and the minimum out-degree orientations of the graph. We introduce the definition of the local out-degree g^*(v) of a vertex v, and show it to be equal to the local density ρ^*(v). We consider the local out-degree to be conceptually simpler, shorter to define, and easier to compute. Using the local out-degree we show a previously unknown fact: that existing algorithms already dynamically approximate the local density for each vertex with polylogarithmic update time. Next, we provide the first distributed algorithms that compute the local density with provable guarantees: given any ε such that ε^{-1} ∈ O(poly n), we show a deterministic distributed algorithm in the LOCAL model where, after O(ε^{-2} log² n) rounds, every vertex v outputs a (1 + ε)-approximation of their local density ρ^*(v). In CONGEST, we show a deterministic distributed algorithm that requires poly(log n,ε^{-1}) ⋅ 2^{O(√{log n})} rounds, which is sublinear in n. As a corollary, we obtain the first deterministic algorithm running in a sublinear number of rounds for (1+ε)-approximate densest subgraph detection in the CONGEST model.
Cite as

Aleksander Bjørn Christiansen, Ivor van der Hoog, and Eva Rotenberg. Local Density and Its Distributed Approximation. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{christiansen_et_al:LIPIcs.STACS.2025.25,
  author =	{Christiansen, Aleksander Bj{\o}rn and van der Hoog, Ivor and Rotenberg, Eva},
  title =	{{Local Density and Its Distributed Approximation}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{25:1--25:20},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-228502},
  doi =		{10.4230/LIPIcs.STACS.2025.25},
  annote =	{Keywords: Distributed graph algorithms, graph density computation, graph density approximation, network analysis theory}
}
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