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We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
In this paper we investigate real-time, dynamic traffic optimization in railway systems. In order to enable practical solution times, we operate the optimizer in a receding horizon fashion and with optimization horizons that are shorter…
We consider the P2P orienteering problem on general metrics and present a (2+{\epsilon}) approximation algorithm. In the stochastic P2P orienteering problem we are given a metric and each node has a fixed reward and random size. The goal is…
This paper will contribute to a practical problem, Urban Traffic. We will investigate those features, try to simplify the complexity and formulize this dynamic system. These contents mainly contain how to analyze a decision problem with…
We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution…
We model and study the problem of assigning traffic in an urban road network infrastructure. In our model, each driver submits their intended destination and is assigned a route to follow that minimizes the social cost (i.e., travel…
We give the first almost-linear total time algorithm for deciding if a flow of cost at most $F$ still exists in a directed graph, with edge costs and capacities, undergoing decremental updates, i.e., edge deletions, capacity decreases, and…
The problem of navigating a bipedal robot to a desired destination in various environments is very important. However, it is very difficult to solve the navigation problem in real time because the computation time is very long due to the…
The ubiquitous expansion and transformation of the energy supply system involves large-scale power infrastructure construction projects. In the view of investments of more than a million dollars per kilometre, planning authorities aim to…
Recommending routes by their probability of having a rider has long been the goal of conventional route recommendation systems. While this maximizes the platform-specific criteria of efficiency, it results in sub-optimal outcomes with the…
Despite the advancement in the technology of autonomous driving cars, the safety of a self-driving car is still a challenging problem that has not been well studied. Motion prediction is one of the core functions of an autonomous driving…
We study the Minimum Crossing Number problem: given an $n$-vertex graph $G$, the goal is to find a drawing of $G$ in the plane with minimum number of edge crossings. This is one of the central problems in topological graph theory, that has…
Predicting the supply and demand of transport systems is vital for efficient traffic management, control, optimization, and planning. For example, predicting where from/to and when people intend to travel by taxi can support fleet managers…
We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…
We propose a flexible gradient tracking approach with adjustable computation and communication steps for solving distributed stochastic optimization problem over networks. The proposed method allows each node to perform multiple local…
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since…
We consider the minimization of edge-crossings in geometric drawings of graphs $G=(V, E)$, i.e., in drawings where each edge is depicted as a line segment. The respective decision problem is NP-hard [Bienstock, '91]. In contrast to theory…
We present polylogarithmic approximation algorithms for variants of the Shortest Path, Group Steiner Tree, and Group ATSP problems with vector costs. In these problems, each edge e has a non-negative vector cost $c_e \in…
Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…