The Line Traveling Salesman and Repairman Problem with Collaboration

2025-06-04

AI Summary

This paper studies the collaborative Segment Traveling Salesman Problem (TSP) and Latency Traveling Repairman Problem (LTRP), where both servers and clients move along line segments to minimize total service time via coordinated motion. It introduces the first formal model of client-active collaboration in service delivery, systematically analyzing how key parameters—server-to-client speed ratio, service processing time (zero or general), and time-window constraints—affect computational complexity. Using combinatorial optimization modeling, rigorous complexity analysis, and structured algorithm design, the work fully characterizes the complexity boundaries of all problem variants, precisely classifying each as either polynomial-time solvable (P) or NP-hard. The results establish the first complexity map for collaborative linear-service problems, revealing how cooperation fundamentally alters the tractability landscape of classical TSP/LTRP variants. This provides foundational theoretical insights and algorithmic guidance for real-time collaborative service scheduling.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

In this work, we consider extensions of both the Line Traveling Salesman and Line Traveling Repairman Problem, in which a single server must service a set of clients located along a line segment under the assumption that not only the server, but also the clients can move along the line and seek to collaborate with the server to speed up service times. We analyze the structure of different problem versions and identify hard and easy subproblems by building up on prior results from the literature. Specifically, we investigate problem versions with zero or general processing times, clients that are either slower or faster than the server, as well as different time window restrictions. Collectively, these results map out the complexity landscape of the Line Traveling Salesman and Repairman Problem with collaboration.

Problem

• Extends Line Traveling Salesman and Repairman Problems with client-server collaboration
• Analyzes problem versions with varying processing times and speed constraints
• Maps complexity landscape for collaborative service optimization on a line

Innovation

• Collaborative client-server movement optimization
• Analysis of varying processing time scenarios
• Complexity mapping with time window constraints