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In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning…
We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the optimum by…
In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…
We give the first algorithm that maintains an approximate decision tree over an arbitrary sequence of insertions and deletions of labeled examples, with strong guarantees on the worst-case running time per update request. For instance, we…
This paper deals with the multiobjective version of the optimal spanning tree problem. More precisely, we are interested in determining the optimal spanning tree according to an Ordered Weighted Average (OWA) of its objective values. We…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
The kTree problem is a special case of Subgraph Isomorphism where the pattern graph is a tree, that is, the input is an $n$-node graph $G$ and a $k$-node tree $T$, and the goal is to determine whether $G$ has a subgraph isomorphic to $T$.…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
In Polyamorous Scheduling, we are given an edge-weighted graph and must find a periodic schedule of matchings in this graph which minimizes the maximal weighted waiting time between consecutive occurrences of the same edge. This NP-hard…
This paper considers the task of learning users' preferences on a combinatorial set of alternatives, as generally used by online configurators, for example. In many settings, only a set of selected alternatives during past interactions is…
We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction…
The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is…
In several applications of automatic diagnosis and active learning a central problem is the evaluation of a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…
This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by…
Policy tree search is a family of tree search algorithms that use a policy to guide the search. These algorithms provide guarantees on the number of expansions required to solve a given problem that are based on the quality of the policy.…
We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…