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Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of horizontal line segments in the Euclidean plane and propose efficient algorithms for optimization problems inspired in two operations on melodies; linear scaling and audio compression. In the scaling problem, an incoming query melody is scaled forward until the similarity measure between the query and a reference melody is minimized. The compression problem asks for a subset of notes of a given melody such that the matching cost between the selected notes and the reference melody is minimized.

This paper proposes a planning algorithm for autonomous media production with multiple Unmanned Aerial Vehicles (UAVs) in outdoor events. Given filming tasks specified by a media Director, we formulate an optimization problem to maximize the filming time considering battery constraints. As we conjecture that the problem is NP-hard, we consider a discretization version, and propose a graph-based algorithm that can find an optimal solution of the discrete problem for a single UAV in polynomial time. Then, a greedy strategy is applied to solve the problem sequentially for multiple UAVs. We demonstrate that our algorithm is efficient for small teams (3-5 UAVs) and that its performance is close to the optimum. We showcase our system in field experiments carrying out actual media production in an outdoor scenario with multiple UAVs., Comment: 7 pages, published in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2020

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 detecting the inherent separations between groups of a given point set in a metric space governed by a similarity function. The pairwise similarities between all data objects form a weighted graph adjacency matrix which contains all necessary information for the clustering process, which can consequently be formulated as a graph partitioning problem. In this context, we propose a new cluster quality measure which uses the maximum spanning tree and allows us to compute the optimal clustering under the min-max principle in polynomial time. Our algorithm can be applied when a load-balanced clustering is required.

We study an optimization problem that arises in the design of covering strategies for multi-robot systems. Consider a team of $n$ cooperating robots traveling along predetermined closed and disjoint trajectories. Each robot needs to periodically communicate information to nearby robots. At places where two trajectories are within range of each other, a communication link is established, allowing two robots to exchange information, provided they are "synchronized", i.e., they visit the link at the same time. In this setting a communication graph is defined and a system of robots is called \emph{synchronized} if every pair of neighbors is synchronized. If one or more robots leave the system, then some trajectories are left unattended. To handle such cases in a synchronized system, when a live robot arrives to a communication link and detects the absence of the neighbor, it shifts to the neighboring trajectory to assume the unattended task. If enough robots leave, it may occur that a live robot enters a state of \emph{starvation}, failing to permanently meet other robots during flight. To measure the tolerance of the system under this phenomenon we define the \emph{$k$-resilience} as the minimum number of robots whose removal may cause $k$ surviving robots to enter a state of starvation. We show that the problem of computing the $k$-resilience is NP-hard if $k$ is part of the input, even if the communication graph is a tree. We propose algorithms to compute the $k$-resilience for constant values of $k$ in general communication graphs and show more efficient algorithms for systems whose communication graph is a tree.