Related papers: An FPTAS for Shortest-Longest Path Problem
The advancement of mobile technologies and the proliferation of map-based applications have enabled a user to access a wide variety of services that range from information queries to navigation systems. Due to the popularity of map-based…
The quadratic shortest path problem (QSPP) is \textcolor{black}{the problem of finding a path with prespecified start vertex $s$ and end vertex $t$ in a digraph} such that the sum of weights of arcs and the sum of interaction costs over all…
An efficient algorithm to solve the $k$ shortest non-homotopic path planning ($k$-SNPP) problem in a 2D environment is proposed in this paper. Motivated by accelerating the inefficient exploration of the homotopy-augmented space of the 2D…
The logic-constrained shortest path problem (LCSPP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC)…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…
The rise of large language models (LLMs) has made natural language-driven route planning an emerging research area that encompasses rich user objectives. Current research exhibits two distinct approaches: direct route planning using…
Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a…
We consider the Travelling Salesman Problem with Neighbourhoods (TSPN) on the Euclidean plane ($\mathbb{R}^2$) and present a Polynomial-Time Approximation Scheme (PTAS) when the neighbourhoods are parallel line segments with lengths between…
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…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
This paper is about the length $X_{\rm MAX}$ of the longest path in directed acyclic graph (DAG) $G=(V,E)$ with random edge lengths, where $|V|=n$ and $|E|=m$. When the edge lengths are mutually independent and uniformly distributed, the…
The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…
A dynamic network ${\cal N} = (G,c,\tau,S)$ where $G=(V,E)$ is a graph, integers $\tau(e)$ and $c(e)$ represent, for each edge $e\in E$, the time required to traverse edge $e$ and its nonnegative capacity, and the set $S\subseteq V$ is a…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
The Collaborative Task Sequencing and Multi-Agent Path Finding (CTS-MAPF) problem requires agents to accomplish sequences of tasks while avoiding collisions, posing significant challenges due to its combinatorial complexity. This work…
We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a…
The Subset-Sums Ratio problem (SSR) is an optimization problem in which, given a set of integers, the goal is to find two subsets such that the ratio of their sums is as close to 1 as possible. In this paper we develop a new FPTAS for the…
Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics.…
Given a graph and a pair of terminals $s$, $t$, the next-to-shortest path problem asks for an $s\!\to \!t$ (simple) path that is shortest among all not shortest $s\!\to \!t$ paths (if one exists). This problem was introduced in 1996, and…