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For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex…
Binary Partition Hierarchies (BPH) and minimum spanning trees are fundamental data structures involved in hierarchical analysis such as quasi-flat zones or watershed. However, classical BPH construction algorithms require to have the whole…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Avraham et al. [AFK+15] presented an alternative approach to parametric search, called \emph{bifurcation}, that performs faster under certain circumstances. Intuitively, when the underlying decider execution can be rolled back cheaply and…
Extracting a Construction Tree from potentially noisy point clouds is an important aspect of Reverse Engineering tasks in Computer Aided Design. Solutions based on algorithmic geometry impose constraints on usable model representations…
We present a new, inductive construction of the Vietoris-Rips complex, in which we take advantage of a small amount of unexploited combinatorial structure in the $k$-skeleton of the complex in order to avoid unnecessary comparisons when…
Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…
The Minimum Quartet Tree Cost problem is to construct an optimal weight tree from the $3{n \choose 4}$ weighted quartet topologies on $n$ objects, where optimality means that the summed weight of the embedded quartet topologies is optimal…
Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…
Partitioning a graph into balanced blocks such that few edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge graphs are streaming algorithms, which use low computational…
Routing is a crucial step in the VLSI design flow. With the advancement of manufacturing technologies, more constraints have emerged in design rules, particularly regarding obstacles during routing, leading to increased routing complexity.…
Information retrieval is a core component of many intelligent systems as it enables conditioning of outputs on new and large-scale datasets. While effective, the standard practice of encoding data into high-dimensional representations for…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Gradient Boosted Decision Trees (GBDTs) are dominant machine learning algorithms for modeling discrete or tabular data. Unlike neural networks with millions of trainable parameters, GBDTs optimize loss function in an additive manner and…
This paper presents a novel algorithm, called MRRT, which uses multiple rapidly-exploring random trees for fast online replanning of autonomous vehicles in dynamic environments with moving obstacles. The proposed algorithm is built upon the…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
Autonomous assembly has been a desired functionality of many intelligent robot systems. We study a new challenging assembly task, designing and constructing a bridge without a blueprint. In this task, the robot needs to first design a…
Finding small vertex covers in a graph has applications in numerous domains. Two common formulations of the problem include: Minimum Vertex Cover, which finds the smallest vertex cover in a graph, and Parameterized Vertex Cover, which finds…
We present a new Markov chain Monte Carlo algorithm, implemented in software Arbores, for inferring the history of a sample of DNA sequences. Our principal innovation is a bridging procedure, previously applied only for simple stochastic…