Document

Track A: Algorithms, Complexity and Games

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

This paper focuses on kernelization algorithms for the fundamental Knapsack problem. A kernelization algorithm (or kernel) is a polynomial-time reduction from a problem onto itself, where the output size is bounded by a function of some problem-specific parameter. Such algorithms provide a theoretical model for data reduction and preprocessing and are central in the area of parameterized complexity. In this way, a kernel for Knapsack for some parameter k reduces any instance of Knapsack to an equivalent instance of size at most f(k) in polynomial time, for some computable function f. When f(k) = k^{O(1)} then we call such a reduction a polynomial kernel.
Our study focuses on two natural parameters for Knapsack: The number w_# of different item weights, and the number p_# of different item profits. Our main technical contribution is a proof showing that Knapsack does not admit a polynomial kernel for any of these two parameters under standard complexity-theoretic assumptions. Our proof discovers an elaborate application of the standard kernelization lower bound framework, and develops along the way novel ideas that should be useful for other problems as well. We complement our lower bounds by showing that Knapsack admits a polynomial kernel for the combined parameter w_# ⋅ p_#.

Klaus Heeger, Danny Hermelin, Matthias Mnich, and Dvir Shabtay. No Polynomial Kernels for Knapsack. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 83:1-83:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{heeger_et_al:LIPIcs.ICALP.2024.83, author = {Heeger, Klaus and Hermelin, Danny and Mnich, Matthias and Shabtay, Dvir}, title = {{No Polynomial Kernels for Knapsack}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {83:1--83:17}, 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.2024.83}, URN = {urn:nbn:de:0030-drops-202261}, doi = {10.4230/LIPIcs.ICALP.2024.83}, annote = {Keywords: Knapsack, polynomial kernels, compositions, number of different weights, number of different profits} }

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

We study single-machine scheduling problems with few deadlines. We focus on two classical objectives, namely minimizing the weighted number of tardy jobs and the total weighted completion time. For both problems, we give a pseudopolynomial-time algorithm for a constant number of different deadlines. This algorithm is complemented with an ETH-based, almost tight lower bound. Furthermore, we study the case where the number of jobs with a nontrivial deadline is taken as parameter. For this case, the complexity of our two problems differ: Minimizing the total number of tardy jobs becomes fixed-parameter tractable, while minimizing the total weighted completion time is W[1]-hard.

Klaus Heeger, Danny Hermelin, and Dvir Shabtay. Single Machine Scheduling with Few Deadlines. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{heeger_et_al:LIPIcs.IPEC.2023.24, author = {Heeger, Klaus and Hermelin, Danny and Shabtay, Dvir}, title = {{Single Machine Scheduling with Few Deadlines}}, booktitle = {18th International Symposium on Parameterized and Exact Computation (IPEC 2023)}, pages = {24:1--24:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-305-8}, ISSN = {1868-8969}, year = {2023}, volume = {285}, editor = {Misra, Neeldhara and Wahlstr\"{o}m, Magnus}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.24}, URN = {urn:nbn:de:0030-drops-194434}, doi = {10.4230/LIPIcs.IPEC.2023.24}, annote = {Keywords: Single-machine scheduling, weighted completion time, tardy jobs, pseudopolynomial algorithms, parameterized complexity} }

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**Published in:** LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

We provide new (parameterized) computational hardness results for Interval Scheduling on Unrelated Machines. It is a classical scheduling problem motivated from just-in-time or lean manufacturing, where the goal is to complete jobs exactly at their deadline. We are given n jobs and m machines. Each job has a deadline, a weight, and a processing time that may be different on each machine. The goal is find a schedule that maximizes the total weight of jobs completed exactly at their deadline. Note that this uniquely defines a processing time interval for each job on each machine.
Interval Scheduling on Unrelated Machines is closely related to coloring interval graphs and has been thoroughly studied for several decades. However, as pointed out by Mnich and van Bevern [Computers & Operations Research, 2018], the parameterized complexity for the number m of machines as a parameter remained open. We resolve this by showing that Interval Scheduling on Unrelated Machines is W[1]-hard when parameterized by the number m of machines. To this end, we prove W[1]-hardness with respect to m of the special case where we have parallel machines with eligible machine sets for jobs. This answers Open Problem 8 of Mnich and van Bevern’s list of 15 open problems in the parameterized complexity of scheduling [Computers & Operations Research, 2018].
Furthermore, we resolve the computational complexity status of the unweighted version of Interval Scheduling on Unrelated Machines by proving that it is NP-complete. This answers an open question by Sung and Vlach [Journal of Scheduling, 2005].

Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Dvir Shabtay. Hardness of Interval Scheduling on Unrelated Machines. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hermelin_et_al:LIPIcs.IPEC.2022.18, author = {Hermelin, Danny and Itzhaki, Yuval and Molter, Hendrik and Shabtay, Dvir}, title = {{Hardness of Interval Scheduling on Unrelated Machines}}, booktitle = {17th International Symposium on Parameterized and Exact Computation (IPEC 2022)}, pages = {18:1--18:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-260-0}, ISSN = {1868-8969}, year = {2022}, volume = {249}, editor = {Dell, Holger and Nederlof, Jesper}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.18}, URN = {urn:nbn:de:0030-drops-173748}, doi = {10.4230/LIPIcs.IPEC.2022.18}, annote = {Keywords: Just-in-time scheduling, Parallel machines, Eligible machine sets, W\lbrack1\rbrack-hardness, NP-hardness} }

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**Published in:** LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. We introduce and investigate the Temporal Δ Independent Set problem, a temporal variant of the well known Independent Set problem. This problem is e.g. motivated in the context of finding conflict-free schedules for maximum subsets of tasks, that have certain (changing) constraints on each day they need to be performed. We are specifically interested in the case where each task needs to be performed in a certain time-interval on each day and two tasks are in conflict on a day if their time-intervals overlap on that day. This leads us to considering Temporal Δ Independent Set on the restricted class of temporal unit interval graphs, i.e., temporal graphs where each layer is unit interval.
We present several hardness results for this problem, as well as two algorithms: The first is a constant-factor approximation algorithm for instances where τ, the total number of time steps (layers) of the temporal graph, and Δ, a parameter that allows us to model some tolerance in the conflicts, are constants. For the second result we use the notion of order preservation for temporal unit interval graphs that, informally, requires the intervals of every layer to obey a common ordering. We provide an FPT algorithm parameterized by the size of minimum vertex deletion set to order preservation.

Danny Hermelin, Yuval Itzhaki, Hendrik Molter, and Rolf Niedermeier. Temporal Unit Interval Independent Sets. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hermelin_et_al:LIPIcs.SAND.2022.19, author = {Hermelin, Danny and Itzhaki, Yuval and Molter, Hendrik and Niedermeier, Rolf}, title = {{Temporal Unit Interval Independent Sets}}, booktitle = {1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)}, pages = {19:1--19:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-224-2}, ISSN = {1868-8969}, year = {2022}, volume = {221}, editor = {Aspnes, James and Michail, Othon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.19}, URN = {urn:nbn:de:0030-drops-159617}, doi = {10.4230/LIPIcs.SAND.2022.19}, annote = {Keywords: Temporal Graphs, Vertex Orderings, Order Preservation, Interval Graphs, Algorithms and Complexity} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Given N instances (X_1,t_1),…,(X_N,t_N) of Subset Sum, the AND Subset Sum problem asks to determine whether all of these instances are yes-instances; that is, whether each set of integers X_i has a subset that sums up to the target integer t_i. We prove that this problem cannot be solved in time Õ((N ⋅ t_max)^{1-ε}), for t_max = max_i t_i and any ε > 0, assuming the ∀ ∃ Strong Exponential Time Hypothesis (∀∃-SETH). We then use this result to exclude Õ(n+P_max⋅n^{1-ε})-time algorithms for several scheduling problems on n jobs with maximum processing time P_max, assuming ∀∃-SETH. These include classical problems such as 1||∑ w_jU_j, the problem of minimizing the total weight of tardy jobs on a single machine, and P₂||∑ U_j, the problem of minimizing the number of tardy jobs on two identical parallel machines.

Amir Abboud, Karl Bringmann, Danny Hermelin, and Dvir Shabtay. Scheduling Lower Bounds via AND Subset Sum. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{abboud_et_al:LIPIcs.ICALP.2020.4, author = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, title = {{Scheduling Lower Bounds via AND Subset Sum}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {4:1--4:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.4}, URN = {urn:nbn:de:0030-drops-124119}, doi = {10.4230/LIPIcs.ICALP.2020.4}, annote = {Keywords: SETH, fine grained complexity, Subset Sum, scheduling} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

This paper is concerned with the 1||∑ p_jU_j problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also a very important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The fastest known pseudo-polynomial time algorithm for the problem is the famous Lawler and Moore algorithm which runs in O(P ⋅ n) time, where P is the total processing time of all n jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date.
In this paper we develop two new algorithms for 1||∑ p_jU_j, each improving on Lawler and Moore’s algorithm in a different scenario:
- Our first algorithm runs in Õ(P^{7/4}) time, and outperforms Lawler and Moore’s algorithm in instances where n = ω̃(P^{3/4}).
- Our second algorithm runs in Õ(min{P ⋅ D_#, P + D}) time, where D_# is the number of different due dates in the instance, and D is the sum of all different due dates. This algorithm improves on Lawler and Moore’s algorithm when n = ω̃(D_#) or n = ω̃(D/P). Further, it extends the known Õ(P) algorithm for the single due date special case of 1||∑ p_jU_j in a natural way.
Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, while for the first algorithm we define a new "skewed" version of (max,min)-convolution which is interesting in its own right.

Karl Bringmann, Nick Fischer, Danny Hermelin, Dvir Shabtay, and Philip Wellnitz. Faster Minimization of Tardy Processing Time on a Single Machine. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bringmann_et_al:LIPIcs.ICALP.2020.19, author = {Bringmann, Karl and Fischer, Nick and Hermelin, Danny and Shabtay, Dvir and Wellnitz, Philip}, title = {{Faster Minimization of Tardy Processing Time on a Single Machine}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {19:1--19:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.19}, URN = {urn:nbn:de:0030-drops-124269}, doi = {10.4230/LIPIcs.ICALP.2020.19}, annote = {Keywords: Weighted number of tardy jobs, sumsets, convolutions} }

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**Published in:** LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

In this paper we consider the p-Norm Hamming Centroid problem which asks to determine whether some given strings have a centroid with a bound on the p-norm of its Hamming distances to the strings. Specifically, given a set S of strings and a real k, we consider the problem of determining whether there exists a string s^* with (sum_{s in S} d^{p}(s^*,s))^(1/p) <=k, where d(,) denotes the Hamming distance metric. This problem has important applications in data clustering and multi-winner committee elections, and is a generalization of the well-known polynomial-time solvable Consensus String (p=1) problem, as well as the NP-hard Closest String (p=infty) problem.
Our main result shows that the problem is NP-hard for all fixed rational p > 1, closing the gap for all rational values of p between 1 and infty. Under standard complexity assumptions the reduction also implies that the problem has no 2^o(n+m)-time or 2^o(k^(p/(p+1)))-time algorithm, where m denotes the number of input strings and n denotes the length of each string, for any fixed p > 1. The first bound matches a straightforward brute-force algorithm. The second bound is tight in the sense that for each fixed epsilon > 0, we provide a 2^(k^(p/((p+1))+epsilon))-time algorithm. In the last part of the paper, we complement our hardness result by presenting a fixed-parameter algorithm and a factor-2 approximation algorithm for the problem.

Jiehua Chen, Danny Hermelin, and Manuel Sorge. On Computing Centroids According to the p-Norms of Hamming Distance Vectors. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chen_et_al:LIPIcs.ESA.2019.28, author = {Chen, Jiehua and Hermelin, Danny and Sorge, Manuel}, title = {{On Computing Centroids According to the p-Norms of Hamming Distance Vectors}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {28:1--28:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola 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.2019.28}, URN = {urn:nbn:de:0030-drops-111495}, doi = {10.4230/LIPIcs.ESA.2019.28}, annote = {Keywords: Strings, Clustering, Multiwinner Election, Hamming Distance} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

The classic Stable Roommates problem (the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint pairs such that no two agents induce a blocking pair. Herein, each agent has a preference list denoting who it prefers to have as a partner, and two agents are blocking if they prefer to be with each other rather than with their assigned partners.
Since stable matchings may not be unique, we study an NP-hard optimization variant of Stable Roommates, called Egal Stable Roommates, which seeks to find a stable matching with a minimum egalitarian cost gamma, i.e. the sum of the dissatisfaction of the agents is minimum. The dissatisfaction of an agent is the number of agents that this agent prefers over its partner if it is matched; otherwise it is the length of its preference list. We also study almost stable matchings, called Min-Block-Pair Stable Roommates, which seeks to find a matching with a minimum number beta of blocking pairs. Our main result is that Egal Stable Roommates parameterized by gamma is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by beta is W[1]-hard, even if the length of each preference list is at most five.

Jiehua Chen, Danny Hermelin, Manuel Sorge, and Harel Yedidsion. How Hard Is It to Satisfy (Almost) All Roommates?. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2018.35, author = {Chen, Jiehua and Hermelin, Danny and Sorge, Manuel and Yedidsion, Harel}, title = {{How Hard Is It to Satisfy (Almost) All Roommates?}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {35:1--35:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.35}, URN = {urn:nbn:de:0030-drops-90398}, doi = {10.4230/LIPIcs.ICALP.2018.35}, annote = {Keywords: NP-hard problems Data reduction rules Kernelizations Parameterized complexity analysis and algorithmics} }

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

In this paper, we study the Connected H-hitting Set and Dominating Set problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the Connected H-hitting set problem, we obtain an \alpha-approximate kernel for every \alpha>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the Dominating Set problem on d-degenerate graphs and provide an interpolation of approximate kernels between the known d^2-approximate kernel of constant size and 1-approximate kernel of size k^{O(d^2)}.

Eduard Eiben, Danny Hermelin, and M. S. Ramanujan. Lossy Kernels for Hitting Subgraphs. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{eiben_et_al:LIPIcs.MFCS.2017.67, author = {Eiben, Eduard and Hermelin, Danny and Ramanujan, M. S.}, title = {{Lossy Kernels for Hitting Subgraphs}}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, pages = {67:1--67:14}, 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.2017.67}, URN = {urn:nbn:de:0030-drops-80955}, doi = {10.4230/LIPIcs.MFCS.2017.67}, annote = {Keywords: parameterized algorithms, lossy kernelization, graph theory} }

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**Published in:** Dagstuhl Reports, Volume 7, Issue 1 (2017)

Dagstuhl Seminar 17041 "Randomization in Parameterized Complexity" took place from January 22nd to January 27th 2017 with the objective to bridge the gap between randomization and parameterized complexity theory. This report documents the talks held during the seminar as well as the open questions arised in the discussion sessions.

Marek Cygan, Fedor V. Fomin, Danny Hermelin, and Magnus Wahlström. Randomization in Parameterized Complexity (Dagstuhl Seminar 17041). In Dagstuhl Reports, Volume 7, Issue 1, pp. 103-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{cygan_et_al:DagRep.7.1.103, author = {Cygan, Marek and Fomin, Fedor V. and Hermelin, Danny and Wahlstr\"{o}m, Magnus}, title = {{Randomization in Parameterized Complexity (Dagstuhl Seminar 17041)}}, pages = {103--128}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2017}, volume = {7}, number = {1}, editor = {Cygan, Marek and Fomin, Fedor V. and Hermelin, Danny and Wahlstr\"{o}m, Magnus}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.1.103}, URN = {urn:nbn:de:0030-drops-72479}, doi = {10.4230/DagRep.7.1.103}, annote = {Keywords: fixed-parameter tractability, intractability, parameterized complexity, randomness} }

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Complete Volume

**Published in:** LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

LIPIcs, Volume 63, IPEC'16, Complete Volume

11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{guo_et_al:LIPIcs.IPEC.2016, title = {{LIPIcs, Volume 63, IPEC'16, Complete Volume}}, booktitle = {11th International Symposium on Parameterized and Exact Computation (IPEC 2016)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-023-1}, ISSN = {1868-8969}, year = {2017}, volume = {63}, editor = {Guo, Jiong and Hermelin, Danny}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016}, URN = {urn:nbn:de:0030-drops-69572}, doi = {10.4230/LIPIcs.IPEC.2016}, annote = {Keywords: Complexity Measures and Classes, Analysis of Algorithms and Problem Complexity, Discrete Mathematics} }

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Front Matter

**Published in:** LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors

11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guo_et_al:LIPIcs.IPEC.2016.0, author = {Guo, Jiong and Hermelin, Danny}, title = {{Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors}}, booktitle = {11th International Symposium on Parameterized and Exact Computation (IPEC 2016)}, pages = {0:i--0:xiv}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-023-1}, ISSN = {1868-8969}, year = {2017}, volume = {63}, editor = {Guo, Jiong and Hermelin, Danny}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.0}, URN = {urn:nbn:de:0030-drops-69180}, doi = {10.4230/LIPIcs.IPEC.2016.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Bodlaender et al.'s [Bodlaender/Jansen/Kratsch,2014] cross-composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of cross-compositions. Our technique makes it possible to prove new no-polynomial-kernel results for a number of problems dealing with length-bounded cuts. Roughly speaking, our new technique combines the advantages of serial and parallel composition. In particular, answering an open question of Golovach and Thilikos [Golovach/Thilikos,2011], we show that, unless NP subseteq coNP/poly, the NP-hard Length-Bounded Edge-Cut problem (delete at most k edges such that the resulting graph has no s-t path of length shorter than l) parameterized by the combination of k and l has no polynomial-size problem kernel. Our framework applies to planar as well as directed variants of the basic problems and also applies to both edge and vertex deletion problems.

Till Fluschnik, Danny Hermelin, André Nichterlein, and Rolf Niedermeier. Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fluschnik_et_al:LIPIcs.ICALP.2016.25, author = {Fluschnik, Till and Hermelin, Danny and Nichterlein, Andr\'{e} and Niedermeier, Rolf}, title = {{Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {25:1--25:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.25}, URN = {urn:nbn:de:0030-drops-63049}, doi = {10.4230/LIPIcs.ICALP.2016.25}, annote = {Keywords: Parameterized complexity, polynomial-time data reduction, cross-compositions, lower bounds, graph modification problems, interdiction problems} }

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**Published in:** LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

We study a scheduling problem where two agents (each equipped with a private set of jobs) compete to perform their respective jobs on a common single machine. Each agent wants to keep the weighted sum of completion times of his jobs below a given (agent-dependent) bound. This problem is known to be NP-hard, even for quite restrictive settings of the problem parameters.
We consider parameterized versions of the problem where one of the agents has a small number of jobs (and where this small number constitutes the parameter). The problem becomes much more tangible in this case, and we present three positive algorithmic results for it. Our study is complemented by showing that the general problem is NP-complete even when one agent only has a single job.

Danny Hermelin, Judith-Madeleine Kubitza, Dvir Shabtay, Nimrod Talmon, and Gerhard Woeginger. Scheduling Two Competing Agents When One Agent Has Significantly Fewer Jobs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 55-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hermelin_et_al:LIPIcs.IPEC.2015.55, author = {Hermelin, Danny and Kubitza, Judith-Madeleine and Shabtay, Dvir and Talmon, Nimrod and Woeginger, Gerhard}, title = {{Scheduling Two Competing Agents When One Agent Has Significantly Fewer Jobs}}, booktitle = {10th International Symposium on Parameterized and Exact Computation (IPEC 2015)}, pages = {55--65}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-92-7}, ISSN = {1868-8969}, year = {2015}, volume = {43}, editor = {Husfeldt, Thore and Kanj, Iyad}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.55}, URN = {urn:nbn:de:0030-drops-55713}, doi = {10.4230/LIPIcs.IPEC.2015.55}, annote = {Keywords: Parameterized Complexity, Multiagent Scheduling} }

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**Published in:** LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

We consider the following graph cut problem called Critical Node Cut (CNC): Given a graph G on n vertices, and two positive integers k and x, determine whether G has a set of k vertices whose removal leaves G with at most x connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in f(kappa) * n^{O(1)} time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters kappa. We consider four such parameters:
- The size k of the required cut.
- The upper bound x on the number of remaining connected pairs.
- The lower bound y on the number of connected pairs to be removed.
- The treewidth w of G.
We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from w+k. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size kappa^{O(1)}, where kappa is the given parameter.

Danny Hermelin, Moshe Kaspi, Christian Komusiewicz, and Barak Navon. Parameterized Complexity of Critical Node Cuts. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 343-354, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hermelin_et_al:LIPIcs.IPEC.2015.343, author = {Hermelin, Danny and Kaspi, Moshe and Komusiewicz, Christian and Navon, Barak}, title = {{Parameterized Complexity of Critical Node Cuts}}, booktitle = {10th International Symposium on Parameterized and Exact Computation (IPEC 2015)}, pages = {343--354}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-92-7}, ISSN = {1868-8969}, year = {2015}, volume = {43}, editor = {Husfeldt, Thore and Kanj, Iyad}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.343}, URN = {urn:nbn:de:0030-drops-55950}, doi = {10.4230/LIPIcs.IPEC.2015.343}, annote = {Keywords: graph cut problem, NP-hard problem, treewidth} }

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**Published in:** LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

We consider the Steiner Multicut problem, which asks, given an undirected graph G, a collection T = \{T_{1},...,T_{t}}, T_i \subseteq V(G), of terminal sets of size at most p, and an integer k, whether there is a set S of at most k edges or nodes such that of each set T_{i} at least one pair of terminals is in different connected components of G \ S. This problem generalizes several well-studied graph cut problems, in particular the Multicut problem, which corresponds to the case p = 2. The Multicut problem was recently shown to be fixed-parameter tractable for parameter k [Marx and Razgon, Bousquet et al., STOC 2011]. The question whether this result generalizes to Steiner Multicut motivates the present work.
We answer the question that motivated this work, and in fact provide a dichotomy of the parameterized complexity of Steiner Multicut on general graphs. That is, for any combination of k, t, p, and the treewidth tw(G) as constant, parameter, or unbounded, and for all versions of the problem (edge deletion and node deletion with and without deletable terminals), we prove either that the problem is fixed-parameter tractable or that the problem is hard (W[1]-hard or even (para-)NP-complete). Among the many results in the paper, we highlight that:
- The edge deletion version of Steiner Multicut is fixed-parameter tractable for parameter k+t on general graphs (but has no polynomial kernel, even on trees).
- In contrast, both node deletion versions of Steiner Multicut are W[1]-hard for the parameter k+t on general graphs.
- All versions of Steiner Multicut are W[1]-hard for the parameter k, even when p=3 and the graph is a tree plus one node.
Since we allow k, t, p, and tw(G) to be any constants, our characterization includes a dichotomy for Steiner Multicut on trees (for tw(G) = 1) as well as a polynomial time versus NP-hardness dichotomy (by restricting k,t,p,tw(G) to constant or unbounded).

Karl Bringmann, Danny Hermelin, Matthias Mnich, and Erik Jan van Leeuwen. Parameterized Complexity Dichotomy for Steiner Multicut. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 157-170, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bringmann_et_al:LIPIcs.STACS.2015.157, author = {Bringmann, Karl and Hermelin, Danny and Mnich, Matthias and van Leeuwen, Erik Jan}, title = {{Parameterized Complexity Dichotomy for Steiner Multicut}}, booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)}, pages = {157--170}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-78-1}, ISSN = {1868-8969}, year = {2015}, volume = {30}, editor = {Mayr, Ernst W. and Ollinger, Nicolas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.157}, URN = {urn:nbn:de:0030-drops-49115}, doi = {10.4230/LIPIcs.STACS.2015.157}, annote = {Keywords: graph cut problems, Steiner cut, fixed-parameter tractability} }

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**Published in:** LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic-programming solution for this problem computes the edit-distance between a pair of strings of total length $O(N)$ in $O(N^2)$ time. To this date, this quadratic upper-bound has never been substantially improved for general strings. However, there are known techniques for breaking this bound in case the strings are known to compress well under a particular compression scheme. The basic idea is to first compress the strings, and then to compute the edit distance between the compressed strings.
As it turns out, practically all known $o(N^2)$ edit-distance algorithms work, in some sense, under the same paradigm described above. It is therefore natural to ask whether there is a single edit-distance algorithm that works for strings which are compressed under any compression scheme. A rephrasing of this question is to ask whether a single algorithm can exploit the compressibility properties of strings under any compression method, even if each string is compressed using a different compression. In this paper we set out to answer this question by using \emph{straight-line programs}. These provide a generic platform for representing many popular compression schemes including the LZ-family, Run-Length Encoding, Byte-Pair Encoding, and dictionary methods.
For two strings of total length $N$ having straight-line program representations of total size $n$, we present an algorithm running in $O(n^{1.4}N^{1.2})$ time for computing the edit-distance of these two strings under any rational scoring function, and an $O(n^{1.34}N^{1.34})$-time algorithm for arbitrary scoring functions. This improves on a recent algorithm of Tiskin that runs in $O(nN^{1.5})$ time, and works only for rational scoring functions.

Danny Hermelin, Gad M. Landau, Shir Landau, and Oren Weimann. A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 529-540, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{hermelin_et_al:LIPIcs.STACS.2009.1804, author = {Hermelin, Danny and Landau, Gad M. and Landau, Shir and Weimann, Oren}, title = {{A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {529--540}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-09-5}, ISSN = {1868-8969}, year = {2009}, volume = {3}, editor = {Albers, Susanne and Marion, Jean-Yves}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1804}, URN = {urn:nbn:de:0030-drops-18040}, doi = {10.4230/LIPIcs.STACS.2009.1804}, annote = {Keywords: Edit distance, Straight-line Programs, Dynamic programming acceleration via compression, Combinatorial pattern matching} }

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