相关论文: Polynomial-time algorithms for Multimarginal Optim…

This paper shows that the semi-dual formulation of the optimal transport problem has a degenerate saddle-point structure, and that its numerical solution is equivalent to solving a constrained optimization problem. We derive necessary and…

We consider the routing flow shop problem with two machines on an asymmetric network. For this problem we discuss properties of an optimal schedule and present a polynomial time algorithm assuming the number of nodes of the network to be…

In an earlier paper of Cadek, Vokrinek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological…

Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…

We present a new algorithm for computing motorcycle graphs that runs in O(n^(4/3+e)) time for any e>0, improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It…

In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…

In this paper we present a robust tracker to solve the multiple object tracking (MOT) problem, under the framework of tracking-by-detection. As the first contribution, we innovatively combine single object tracking (SOT) algorithms with…

Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…

Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to…

We generalize the polynomial-time solvability of $k$-\textsc{Diverse Minimum s-t Cuts} (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three…

Trajectory optimization is an important tool for control and planning of complex, underactuated robots, and has shown impressive results in real world robotic tasks. However, in applications where the cost function to be optimized is…

It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…

Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate…

We consider the problem of finding patrol schedules for $k$ robots to visit a given set of $n$ sites in a metric space. Each robot has the same maximum speed and the goal is to minimize the weighted maximum latency of any site, where the…

This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…

We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…

This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…

Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…