相关论文: Polynomial-time algorithms for Multimarginal Optim…
We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of…
Autonomous navigation requires robots to generate trajectories for collision avoidance efficiently. Although plenty of previous works have proven successful in generating smooth and spatially collision-free trajectories, their solutions…
The use of optimal transport (OT) distances, and in particular entropic-regularised OT distances, is an increasingly popular evaluation metric in many areas of machine learning and data science. Their use has largely been driven by the…
The $k$-opt algorithm is one of the simplest and most widely used heuristics for solving the traveling salesman problem. Starting from an arbitrary tour, the $k$-opt algorithm improves the current tour in each iteration by exchanging up to…
The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…
We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing…
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete…
We provide faster strongly polynomial time algorithms solving maximum flow in structured $n$-node $m$-arc networks. Our results imply an $n^{\omega + o(1)}$-time strongly polynomial time algorithms for computing a maximum bipartite…
We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is…
We consider the problem of computing a Steiner tree of minimum cost under a hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
We present a pseudopolynomial-time algorithm for the Knapsack problem that has running time $\widetilde{O}(n + t\sqrt{p_{\max}})$, where $n$ is the number of items, $t$ is the knapsack capacity, and $p_{\max}$ is the maximum item profit.…
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
This paper addresses the problem of enumerating all supported efficient solutions for a linear multi-objective integer minimum cost flow problem (MOIMCF). It derives an output-polynomial time algorithm to determine all supported efficient…