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We observe that a standard transformation between \emph{ordinal} trees (arbitrary rooted trees with ordered children) and binary trees leads to interesting succinct binary tree representations. There are four symmetric versions of these…
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or…
The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as…
For a tree $T$, let $lp(T)$ be the number of different lengths of leaf to leaf paths in $T$. For a degree sequence $s$ of a tree, let ${\rm rad}(s)$ be the minimum radius of a tree with degree sequence $s$. Recently, Di Braccio,…
We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree,…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
The efficiency of sampling-based motion planning brings wide application in autonomous mobile robots. The conventional rapidly exploring random tree (RRT) algorithm and its variants have gained significant successes, but there are still…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…
Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be…
We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of $m$ binary trees with…
We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and maximum flow algorithms. Since being introduced by Edmonds and Karp in 1972, it has been widely applied in many different settings.…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean $p\leq1/2$. How many of these Bernoullis one must look at in order to find a path of length $n$ from the root which maximizes, up…
The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…