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In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
In this paper we address the speed planning problem for a vehicle over an assigned path with the aim of minimizing a weighted sum of travel time and energy consumption under suitable constraints (maximum allowed speed, maximum traction or…
In this paper, we present an online method for converting an arbitrary geometric path represented by a sequence of states, generated by any planner (e.g., sampling-based planners like RRT or PRM, search-based planners like ARA*, etc.), into…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Fixed-point iteration algorithms like RTA (response time analysis) and QPA (quick processor-demand analysis) are arguably the most popular ways of solving schedulability problems for preemptive uniprocessor FP (fixed-priority) and EDF…
This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
In this work, we develop a fast hierarchical solver for solving large, sparse least squares problems. We build upon the algorithm, spaQR (sparsified QR), that was developed by the authors to solve large sparse linear systems. Our algorithm…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its…
Trajectory simplification is a problem encountered in areas like Robot programming by demonstration, CAD/CAM, computer vision, and in GPS-based applications like traffic analysis. This problem entails reduction of the points in a given…
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…
In this paper, we present a computationally efficient trajectory optimizer that can exploit GPUs to jointly compute trajectories of tens of agents in under a second. At the heart of our optimizer is a novel reformulation of the non-convex…
Motivated by multi-domain service function chain (SFC) orchestration, we define the shortest-longest path (SLP) problem, prove its hardness, and design an efficient fully polynomial time approximation scheme (FPTAS) using the dynamic…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
This paper considers the collision avoidance problem in a multi-agent multi-obstacle framework. The originality in solving this intensively studied problem resides in the proposed geometrical view combined with differential flatness for…