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Fionn Mc Inerney

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17 papers
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17

IJCAI Conference 2025 Conference Paper

A Structural Complexity Analysis of Hierarchical Task Network Planning

  • Cornelius Brand
  • Robert Ganian
  • Fionn Mc Inerney
  • Simon Wietheger

We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be reached. Our focus lies on identifying structural properties which yield tractability. We obtain new polynomial algorithms for all three problems on a natural class of primitive networks, along with corresponding lower bounds. We also obtain an algorithmic meta-theorem for lifting polynomial-time solvability from primitive to general task networks, and prove that its preconditions are tight. Finally, we analyze the parameterized complexity of the three problems.

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AAAI Conference 2025 Conference Paper

Parameterized Complexity of Caching in Networks

  • Robert Ganian
  • Fionn Mc Inerney
  • Dimitra Tsigkari

The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research areas - including not only content delivery, but also edge intelligence and inference - and the extensive body of work on empirical aspects of caching, very little is known about the exact boundaries of tractability for the problem beyond its general NP-hardness. We close this gap by performing a comprehensive complexity-theoretic analysis of the problem through the lens of the parameterized complexity paradigm, which is designed to provide more precise statements regarding algorithmic tractability than classical complexity. Our results include algorithmic lower and upper bounds which together establish the conditions under which the caching problem becomes tractable.

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ICLR Conference 2025 Conference Paper

The Computational Complexity of Positive Non-Clashing Teaching in Graphs

  • Robert Ganian
  • Liana Khazaliya
  • Fionn Mc Inerney
  • Mathis Rocton

We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner under the considered, previously established model. For any class of concepts, it is known that this problem can be effortlessly transferred to the setting of balls in a graph $G$. We establish (1) the NP-hardness of the problem even when restricted to instances with positive non-clashing teaching dimension $k=2$ and where all balls in the graph are present, (2) near-tight running time upper and lower bounds for the problem on general graphs, (3) fixed-parameter tractability when parameterized by the vertex integrity of $G$, and (4) a lower bound excluding fixed-parameter tractability when parameterized by the feedback vertex number and pathwidth of $G$, even when combined with $k$. Our results provide a nearly complete understanding of the complexity landscape of computing the positive non-clashing teaching dimension and answer open questions from the literature.

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NeurIPS Conference 2025 Conference Paper

The Parameterized Complexity of Computing the VC-Dimension

  • Florent Foucaud
  • Harmender Gahlawat
  • Fionn Mc Inerney
  • Prafullkumar Tale

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In particular, given a hypergraph $\mathcal{H}=(\mathcal{V}, \mathcal{E})$, we prove that the naive $2^{\mathcal{O}(|\mathcal{V}|)}$-time algorithm is asymptotically tight under the Exponential Time Hypothesis (ETH). We then prove that the problem admits a $1$-additive fixed-parameter approximation algorithm when parameterized by the maximum degree of $\mathcal{H}$ and a fixed-parameter algorithm when parameterized by its dimension, and that these are essentially the only such exploitable structural parameters. Lastly, we consider a generalization of the problem, formulated using graphs, which captures the VC-dimension of both set systems and graphs. We design a $2^{\mathcal{O}(\texttt{tw}\cdot \log \texttt{tw})}\cdot |V|$-time algorithm for any graph $G=(V, E)$ of treewidth $\texttt{tw}$ (which, for a set system, applies to the treewidth of its incidence graph). This is in contrast with closely related problems that require a double-exponential dependency on the treewidth (assuming the ETH).

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AAAI Conference 2024 Conference Paper

The Complexity of Optimizing Atomic Congestion

  • Cornelius Brand
  • Robert Ganian
  • Subrahmanyam Kalyanasundaram
  • Fionn Mc Inerney

Atomic congestion games are a classic topic in network design, routing, and algorithmic game theory, and are capable of modeling congestion and flow optimization tasks in various application areas. While both the price of anarchy for such games as well as the computational complexity of computing their Nash equilibria are by now well-understood, the computational complexity of computing a system-optimal set of strategies - that is, a centrally planned routing that minimizes the average cost of agents - is severely understudied in the literature. We close this gap by identifying the exact boundaries of tractability for the problem through the lens of the parameterized complexity paradigm. After showing that the problem remains highly intractable even on extremely simple networks, we obtain a set of results which demonstrate that the structural parameters which control the computational (in)tractability of the problem are not vertex-separator based in nature (such as, e.g., treewidth), but rather based on edge separators. We conclude by extending our analysis towards the (even more challenging) min-max variant of the problem.

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MFCS Conference 2022 Conference Paper

Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters

  • Esther Galby
  • Liana Khazaliya
  • Fionn Mc Inerney
  • Roohani Sharma
  • Prafullkumar Tale

For a graph G, a subset S ⊆ V(G) is called a resolving set if for any two vertices u, v ∈ V(G), there exists a vertex w ∈ S such that d(w, u) ≠ d(w, v). The Metric Dimension problem takes as input a graph G and a positive integer k, and asks whether there exists a resolving set of size at most k. This problem was introduced in the 1970s and is known to be NP-hard [GT 61 in Garey and Johnson’s book]. In the realm of parameterized complexity, Hartung and Nichterlein [CCC 2013] proved that the problem is W[2]-hard when parameterized by the natural parameter k. They also observed that it is FPT when parameterized by the vertex cover number and asked about its complexity under smaller parameters, in particular the feedback vertex set number. We answer this question by proving that Metric Dimension is W[1]-hard when parameterized by the feedback vertex set number. This also improves the result of Bonnet and Purohit [IPEC 2019] which states that the problem is W[1]-hard parameterized by the treewidth. Regarding the parameterization by the vertex cover number, we prove that Metric Dimension does not admit a polynomial kernel under this parameterization unless NP ⊆ coNP/poly. We observe that a similar result holds when the parameter is the distance to clique. On the positive side, we show that Metric Dimension is FPT when parameterized by either the distance to cluster or the distance to co-cluster, both of which are smaller parameters than the vertex cover number.

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MFCS Conference 2022 Conference Paper

Sample Compression Schemes for Balls in Graphs

  • Jérémie Chalopin
  • Victor Chepoi
  • Fionn Mc Inerney
  • Sébastien Ratel
  • Yann Vaxès

One of the open problems in machine learning is whether any set-family of VC-dimension d admits a sample compression scheme of size O(d). In this paper, we study this problem for balls in graphs. For balls of arbitrary radius r, we design proper sample compression schemes of size 4 for interval graphs, of size 6 for trees of cycles, and of size 22 for cube-free median graphs. We also design approximate sample compression schemes of size 2 for balls of δ-hyperbolic graphs.

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