Author name cluster

Till Fluschnik

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9 papers

2 author rows

ECAI Conference 2025 Conference Paper

Properties of Egalitarian Sequences of Committees: Theory and Experiments

Paula Böhm
Robert Bredereck
Till Fluschnik

We study the task of electing egalitarian sequences of τ committees given a set of agents with additive utilities for candidates available on each of τ levels. We introduce several rules for electing an egalitarian committee sequence as well as properties for such rules. We settle the computational complexity of finding a winning sequence for our rules and classify them against our properties. Additionally, we transform sequential election data from existing election data from the literature. Using this data set, we compare our rules empirically and test them experimentally against our properties.

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AAAI Conference 2024 Conference Paper

Locally Rainbow Paths

Till Fluschnik
Leon Kellerhals
Malte Renken

We introduce the algorithmic problem of finding a locally rainbow path of length l connecting two distinguished vertices s and t in a vertex-colored directed graph. Herein, a path is locally rainbow if between any two visits of equally colored vertices, the path traverses consecutively at leaset r differently colored vertices. This problem generalizes the well-known problem of finding a rainbow path. It finds natural applications whenever there are different types of resources that must be protected from overuse, such as crop sequence optimization or production process scheduling. We show that the problem is computationally intractable even if r=2 or if one looks for a locally rainbow among the shortest paths. On the positive side, if one looks for a path that takes only a short detour (i.e., it is slightly longer than the shortest path) and if r is small, the problem can be solved efficiently. Indeed, the running time of the respective algorithm is near-optimal unless the ETH fails.

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IJCAI Conference 2023 Conference Paper

Algorithmics of Egalitarian versus Equitable Sequences of Committees

Eva Michelle Deltl
Till Fluschnik
Robert Bredereck

We study the election of sequences of committees, where in each of tau levels (e. g. modeling points in time) a committee consisting of k candidates from a common set of m candidates is selected. For each level, each of n agents (voters) may nominate one candidate whose selection would satisfy her. We are interested in committees which are good with respect to the satisfaction per day and per agent. More precisely, we look for egalitarian or equitable committee sequences. While both guarantee that at least x agents per day are satisfied, egalitarian committee sequences ensure that each agent is satisfied in at least y levels while equitable committee sequences ensure that each agent is satisfied in exactly y levels. We analyze the parameterized complexity of finding such committees for the parameters n, m, k, tau, x, and y, as well as combinations thereof.

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ECAI Conference 2023 Conference Paper

Efficiently Computing Smallest Agreeable Sets

Robert Bredereck
Till Fluschnik
Nimrod Talmon

We study the computational complexity of identifying a small agreeable subset of items. A subset of items is agreeable if every agent does not prefer its complement set. We study settings in which agents either can assign arbitrary utilities to the items; can approve or disapprove the items; or can rank the items (in which case we consider Borda utilities). We prove that deciding whether an agreeable set exists is NP-hard for all variants; and we perform a parameterized analysis regarding the following natural parameters: the number of agents, the number of items, and the upper bound on the size of the agreeable set in question.

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IJCAI Conference 2022 Conference Paper

Placing Green Bridges Optimally, with Habitats Inducing Cycles

Maike Herkenrath
Till Fluschnik
Francesco Grothe
Leon Kellerhals

Choosing the placement of wildlife crossings (i. e. , green bridges) to reconnect animal species' fragmented habitats is among the 17 goals towards sustainable development by the UN. We consider the following established model: Given a graph whose vertices represent the fragmented habitat areas and whose weighted edges represent possible green bridge locations, as well as the habitable vertex set for each species, find the cheapest set of edges such that each species' habitat is connected. We study this problem from a theoretical (algorithms and complexity) and an experimental perspective, while focusing on the case where habitats induce cycles. We prove that the NP-hardness persists in this case even if the graph structure is restricted. If the habitats additionally induce faces in plane graphs however, the problem becomes efficiently solvable. In our empirical evaluation we compare this algorithm as well as ILP formulations for more general variants and an approximation algorithm with another. Our evaluation underlines that each specialization is beneficial in terms of running time, whereas the approximation provides highly competitive solutions in practice.

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IJCAI Conference 2022 Conference Paper

When Votes Change and Committees Should (Not)

Robert Bredereck
Till Fluschnik
Andrzej Kaczmarczyk

Electing a single committee of a small size is a classical and well-understood voting situation. Being interested in a sequence of committees, we introduce two time-dependent multistage models based on simple scoring-based voting. Therein, we are given a sequence of voting profiles (stages) over the same set of agents and candidates, and our task is to find a small committee for each stage of high score. In the conservative model we additionally require that any two consecutive committees have a small symmetric difference. Analogously, in the revolutionary model we require large symmetric differences. We prove both models to be NP-hard even for a constant number of agents, and, based on this, initiate a parameterized complexity analysis for the most natural parameters and combinations thereof. Among other results, we prove both models to be in XP yet W[1]-hard regarding the number of stages, and that being revolutionary seems to be "easier" than being conservative.

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TCS Journal 2020 Journal Article

Temporal graph classes: A view through temporal separators

Till Fluschnik
Hendrik Molter
Rolf Niedermeier
Malte Renken
Philipp Zschoche

We investigate for temporal graphs the computational complexity of separating two distinct vertices s and z by vertex deletion. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding Temporal ( s, z ) -Separation problem is NP-complete, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph—there we observe polynomial-time solvability in the case of bounded treewidth—as well as restrictions concerning the “temporal evolution” along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases.

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AAAI Conference 2019 Conference Paper

Fair Knapsack

Till Fluschnik
Piotr Skowron
Mervin Triphaus
Kai Wilker

We study the following multiagent variant of the knapsack problem. We are given a set of items, a set of voters, and a value of the budget; each item is endowed with a cost and each voter assigns to each item a certain value. The goal is to select a subset of items with the total cost not exceeding the budget, in a way that is consistent with the voters’ preferences. Since the preferences of the voters over the items can vary significantly, we need a way of aggregating these preferences, in order to select the socially best valid knapsack. We study three approaches to aggregating voters’ preferences, which are motivated by the literature on multiwinner elections and fair allocation. This way we introduce the concepts of individually best, diverse, and fair knapsack. We study the computational complexity (including parameterized complexity, and complexity under restricted domains) of the aforementioned multiagent variants of knapsack.

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MFCS Conference 2018 Conference Paper

The Complexity of Finding Small Separators in Temporal Graphs

Philipp Zschoche
Till Fluschnik
Hendrik Molter
Rolf Niedermeier

Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths connecting one terminal to the other. Herein, we consider two models of temporal paths: paths that pass through arbitrarily many edges per time step (non-strict) and paths that pass through at most one edge per time step (strict). Regarding the number of time steps of a temporal graph, we show a complexity dichotomy (NP-hardness versus polynomial-time solvability) for both problem variants. Moreover we prove both problem variants to be NP-complete even on temporal graphs whose underlying graph is planar. We further show that, on temporal graphs with planar underlying graph, if additionally the number of time steps is constant, then the problem variant for strict paths is solvable in quasi-linear time. Finally, we introduce and motivate the notion of a temporal core (vertices whose incident edges change over time). We prove that the non-strict variant is fixed-parameter tractable when parameterized by the size of the temporal core, while the strict variant remains NP-complete, even for constant-size temporal cores.

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