相关论文: An Approximation Algorithm for Stackelberg Network…

The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…

We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…

The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…

We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of $\frac{e}{e-1}$, and provide a…

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…

In this paper we study the routing and rebalancing problem for a fleet of autonomous vehicles providing on-demand transportation within a congested urban road network (that is, a road network where traffic speed depends on vehicle density).…

Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…

We consider a stylized formal model of public transportation, where a set of agents need to travel along a given road, and there is a bus that runs the length of this road. Each agent has a left terminal and a right terminal between which…

We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…

We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…

The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…

We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…

We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…

We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…

This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…

Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and…

We consider the stochastic $k$-TSP problem where rewards at vertices are random and the objective is to minimize the expected length of a tour that collects reward $k$. We present an adaptive $O(\log k)$-approximation algorithm, and a…

The ridesharing problem is that given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements, select a subset of trips and use the vehicles of selected trips to deliver all individuals to…