We study the complexity of candidate control in participatory budgeting elections. The goal of constructive candidate control is to ensure that a given candidate wins by either adding or deleting candidates from the election (in the destructive setting, the goal is to prevent a given candidate from winning). We show that such control problems are NP-hard to solve for many participatory budgeting voting rules, including Phragmén and Equal-Shares, but there are natural cases with polynomial-time algorithms. We also argue that control by deleting candidates is a useful tool for assessing the performance (or, strength) of initially losing projects, and we support this view with experiments on real-life PB instances.

In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we study self-deleting graphs, introduced by Carmesin et al. [Sarah Carmesin et al., 2023], which consist of a graph G = (V, E) and a function f: V → 2^E, where f(v) is the set of edges that will be deleted after visiting the vertex v. In the (Shortest) Self-Deleting s-t-path problem we are given a self-deleting graph and its vertices s and t, and we are asked to find a (shortest) path from s to t, such that it does not traverse an edge in f(v) after visiting v for any vertex v. We prove that Self-Deleting s-t-path is NP-hard even if the given graph is outerplanar, bipartite, has maximum degree 3, bandwidth 2 and |f(v)| ≤ 1 for each vertex v. We show that Shortest Self-Deleting s-t-path is W[1]-complete parameterized by the length of the sought path and that Self-Deleting s-t-path is W[1]-complete parameterized by the vertex cover number, feedback vertex set number and treedepth. We also show that the problem becomes FPT when we parameterize by the maximum size of f(v) and several structural parameters. Lastly, we show that the problem does not admit a polynomial kernel even for parameterization by the vertex cover number and the maximum size of f(v) combined already on 2-outerplanar graphs.

In the Equitable Connected Partition (ECP for short) problem, we are given a graph G = (V,E) together with an integer p ∈ ℕ, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G and the size of each two parts differs by at most 1. On the one hand, the problem is known to be NP-hard in general and W[1]-hard with respect to the path-width, the feedback-vertex set, and the number of parts p combined. On the other hand, fixed-parameter algorithms are known for parameters the vertex-integrity and the max leaf number. In this work, we systematically study ECP with respect to various structural restrictions of the underlying graph and provide a clear dichotomy of its parameterised complexity. Specifically, we show that the problem is in FPT when parameterized by the modular-width and the distance to clique. Next, we prove W[1]-hardness with respect to the distance to cluster, the 4-path vertex cover number, the distance to disjoint paths, and the feedback-edge set, and NP-hardness for constant shrub-depth graphs. Our hardness results are complemented by matching algorithmic upper-bounds: we give an XP algorithm for parameterisation by the tree-width and the distance to cluster. We also give an improved FPT algorithm for parameterisation by the vertex integrity and the first explicit FPT algorithm for the 3-path vertex cover number. The main ingredient of these algorithms is a formulation of ECP as N-fold IP, which clearly indicates that such formulations may, in certain scenarios, significantly outperform existing algorithms based on the famous algorithm of Lenstra.

Microaggregation is a classical statistical disclosure control technique which requires the input data to be partitioned into clusters while adhering to specified size constraints. We provide novel exact algorithms and lower bounds for the task of microaggregating a given network while considering both unrestricted and connected clusterings, and analyze these from the perspective of the parameterized complexity paradigm. Altogether, our results assemble a complete complexity-theoretic picture for the network microaggregation problem with respect to the most natural parameterizations of the problem, including input-specified parameters capturing the size and homogeneity of the clusters as well as the treewidth and vertex cover number of the network.