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Nowadays new technologies, and especially artificial intelligence, are more and more established in our society. Big data analysis and machine learning, two sub-fields of artificial intelligence, are at the core of many recent breakthroughs…

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…

In the Vertex Planarization problem one asks to delete the minimum possible number of vertices from an input graph to obtain a planar graph. The parameterized complexity of this problem, parameterized by the solution size (the number of…

Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known…

This paper studies the important problem of finding all $k$-nearest neighbors to points of a query set $Q$ in another reference set $R$ within any metric space. Our previous work defined compressed cover trees and corrected the key…

Structured prediction is a powerful framework for coping with joint prediction of interacting outputs. A central difficulty in using this framework is that often the correct label dependence structure is unknown. At the same time, we would…

'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…

The Steiner Multicut problem asks, given an undirected graph G, terminals sets T1,...,Tt $\subseteq$ V(G) of size at most p, and an integer k, whether there is a set S of at most k edges or nodes s.t. of each set Ti at least one pair of…

Graph Burning asks, given a graph $G = (V,E)$ and an integer $k$, whether there exists $(b_{0},\dots,b_{k-1}) \in V^{k}$ such that every vertex in $G$ has distance at most $i$ from some $b_{i}$. This problem is known to be NP-complete even…

A long line of research on fixed parameter tractability of integer programming culminated with showing that integer programs with n variables and a constraint matrix with dual tree-depth d and largest entry D are solvable in time…

In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projected variables, where multiple solutions that are identical when…

We study the well-known Vertex Cover problem parameterized above and below tight bounds. We show that two of the parameterizations (both were suggested by Mahajan, Raman and Sikdar, J. Computer and System Sciences, 75(2):137--153, 2009) are…

For a phylogenetic tree, the phylogenetic diversity of a set A of taxa is the total weight of edges on paths to A. Finding small sets of maximal diversity is crucial for conservation planning, as it indicates where limited resources can be…

In this paper, we estimate the weak saturation numbers of trees. As a case study, we examine caterpillars and obtain several tight estimates. In particular, this implies that for any $\alpha\in [1,2]$, there exist caterpillars with $k$…

Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…

Many hard problems in the computational sciences are equivalent to counting the leaves of a decision tree, or, more generally, summing a cost function over the nodes. These problems include calculating the permanent of a matrix, finding the…

Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…

We associate a graph with a 1-safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]-hardness results for many problems about 1-safe…

We present efficient combinatorial parameterized algorithms for several classical graph-based counting problems in computational chemistry, including (i) Kekule structures, (ii) the Hosoya index, (iii) the Merrifield-Simmons index, and (iv)…

We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large…