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View article: Parameterized Complexity of Temporal Connected Components: Treewidth and k-Path Graphs
Parameterized Complexity of Temporal Connected Components: Treewidth and k-Path Graphs Open
We study the parameterized complexity of maximum temporal connected components (tccs) in temporal graphs, i.e., graphs that deterministically change over time. In a tcc, any pair of vertices must be able to reach each other via a time-resp…
View article: Determinantal Sieving
Determinantal Sieving Open
We introduce determinantal sieving, a new, remarkably powerful tool in the toolbox of algebraic FPT algorithms. Given a polynomial $P(X)$ on a set of variables $X=\{x_1,\ldots,x_n\}$ and a linear matroid $M=(X,\mathcal{I})$ of rank $k$, bo…
View article: The Complexity of Extending Fair Allocations of Indivisible Goods
The Complexity of Extending Fair Allocations of Indivisible Goods Open
We initiate the study of computing envy-free allocations of indivisible items in the extension setting, i.e., when some part of the allocation is fixed and the task is to allocate the remaining items. In view of the NP-hardness of the prob…
View article: How Many Lines to Paint the City: Exact Edge-Cover in Temporal Graphs
How Many Lines to Paint the City: Exact Edge-Cover in Temporal Graphs Open
Logistics and transportation networks require a large amount of resources to realise necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connection…
View article: Balanced and Fair Partitioning of Friends
Balanced and Fair Partitioning of Friends Open
In the recently introduced model of fair partitioning of friends, there is a set of agents located on the vertices of an underlying graph that indicates the friendships between the agents. The task is to partition the graph into k balanced…
View article: Balanced and Fair Partitioning of Friends
Balanced and Fair Partitioning of Friends Open
In the recently introduced model of fair partitioning of friends, there is a set of agents located on the vertices of an underlying graph that indicates the friendships between the agents. The task is to partition the graph into $k$ balanc…
View article: The Complexity of Extending Fair Allocations of Indivisible Goods
The Complexity of Extending Fair Allocations of Indivisible Goods Open
We initiate the study of computing envy-free allocations of indivisible items in the extension setting, i.e., when some part of the allocation is fixed and the task is to allocate the remaining items. Given the known NP-hardness of the pro…
View article: FPT algorithms over linear delta-matroids with applications
FPT algorithms over linear delta-matroids with applications Open
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures s…
View article: Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion
Polynomial Kernel and Incompressibility for Prison-Free Edge Deletion and Completion Open
Given a graph $G$ and an integer $k$, the $H$-free Edge Deletion problem asks whether there exists a set of at most $k$ edges of $G$ whose deletion makes $G$ free of induced copies of $H$. Significant attention has been given to the kernel…
View article: Bi-objective Optimization in Role Mining
Bi-objective Optimization in Role Mining Open
Role mining is a technique that is used to derive a role-based authorization policy from an existing policy. Given a set of users U , a set of permissions P , and a user–permission authorization relation \(\mathit {UPA} \subseteq U \times …
View article: EF1 and EFX Orientations
EF1 and EFX Orientations Open
We study the problem of finding fair allocations -- EF1 and EFX -- of indivisible goods with orientations. In an orientation, every agent gets items from their own predetermined set. For EF1, we show that EF1 orientations always exist when…
View article: How Many Lines to Paint the City: Exact Edge-Cover in Temporal Graphs
How Many Lines to Paint the City: Exact Edge-Cover in Temporal Graphs Open
Logistics and transportation networks require a large amount of resources to realize necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connection…
View article: From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem
From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem Open
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently formula…
View article: Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy
Parameterized Algorithms for Coordinated Motion Planning: Minimizing Energy Open
We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of $k$ robots to their destinations with the aim of minimizing the…
View article: Individual Rationality in Topological Distance Games is Surprisingly Hard
Individual Rationality in Topological Distance Games is Surprisingly Hard Open
In the recently introduced topological distance games, strategic agents need to be assigned to a subset of vertices of a topology. In the assignment, the utility of an agent depends on both the agent's inherent utilities for other agents a…
View article: Bi-objective Optimization in Role Mining
Bi-objective Optimization in Role Mining Open
Role mining is a technique used to derive a role-based authorization policy from an existing policy. Given a set of users $U$, a set of permissions $P$ and a user-permission authorization relation $\mahtit{UPA}\subseteq U\times P$, a role …
View article: Learning Small Decision Trees for Data of Low Rank-Width
Learning Small Decision Trees for Data of Low Rank-Width Open
We consider the NP-hard problem of finding a smallest decision tree representing a classification instance in terms of a partially defined Boolean function. Small decision trees are desirable to provide an interpretable model for the given…
View article: The Complexity of Fair Division of Indivisible Items with Externalities
The Complexity of Fair Division of Indivisible Items with Externalities Open
We study the computational complexity of fairly allocating a set of indivisible items under externalities. In this recently-proposed setting, in addition to the utility the agent gets from their bundle, they also receive utility from items…
View article: The Computational Complexity of Concise Hypersphere Classification
The Computational Complexity of Concise Hypersphere Classification Open
Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued and binary data. However, obtaining an (ideally concise) explanation via hypersphere clas…
View article: The Complexity of Envy-Free Graph Cutting
The Complexity of Envy-Free Graph Cutting Open
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be as…
View article: A Structural Complexity Analysis of Synchronous Dynamical Systems
A Structural Complexity Analysis of Synchronous Dynamical Systems Open
Synchronous dynamic systems are well-established models that have been used to capture a range of phenomena in networks, including opinion diffusion, spread of disease and product adoption. We study the three most notable problems in synch…
View article: The Parameterized Complexity of Coordinated Motion Planning
The Parameterized Complexity of Coordinated Motion Planning Open
In Coordinated Motion Planning (CMP), we are given a rectangular-grid on which $k$ robots occupy $k$ distinct starting gridpoints and need to reach $k$ distinct destination gridpoints. In each time step, any robot may move to a neighboring…
View article: Finding a Cluster in Incomplete Data
Finding a Cluster in Incomplete Data Open
We study two variants of the fundamental problem of finding a cluster in incomplete data. In the problems under consideration, we are given a multiset of incomplete $d$-dimensional vectors over the binary domain and integers $k$ and $r$, a…
View article: Some coordination problems are harder than others
Some coordination problems are harder than others Open
In order to coordinate players in a game must first identify a target pattern of behaviour. In this paper we investigate the difficulty of identifying prominent outcomes in two kinds of binary action coordination problems in social network…
View article: Highly Connected Steiner Subgraph -- Parameterized Algorithms and Applications to Hitting Set Problems
Highly Connected Steiner Subgraph -- Parameterized Algorithms and Applications to Hitting Set Problems Open
Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. Thi…
View article: The Complexity of Fair Division of Indivisible Items with Externalities
The Complexity of Fair Division of Indivisible Items with Externalities Open
We study the computational complexity of fairly allocating a set of indivisible items under externalities. In this recently-proposed setting, in addition to the utility the agent gets from their bundle, they also receive utility from items…
View article: Learning Small Decision Trees with Large Domain
Learning Small Decision Trees with Large Domain Open
One favors decision trees (DTs) of the smallest size or depth to facilitate explainability and interpretability. However, learning such an optimal DT from data is well-known to be NP-hard. To overcome this complexity barrier, Ordyniak and …