Optimizing Distances for Multi-Broadcast in Temporal Graphs

2026-02-12

AI Summary

This study addresses the multi-source broadcast scheduling problem in temporal graphs, aiming to schedule edge availabilities so as to cover all vertices while minimizing a given temporal distance metric in the worst case. The authors systematically analyze the computational complexity and approximability of six temporal distance measures, including Earliest-Arrival (EA) and Latest-Departure (LD). A key contribution is the identification of fundamental differences between single-source and multi-source settings: under a single source, EA and LD are polynomial-time solvable, whereas the remaining four metrics are NP-hard. For the Fastest (FT) and Minimum-Wait (MW) metrics, the paper presents approximation algorithms. Furthermore, it establishes structural conditions on the underlying graph that guarantee feasibility for multi-source EA and LD scheduling.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements

Abstract

Temporal graphs represent networks in which connections change over time, with edges available only at specific moments. Motivated by applications in logistics, multi-agent information spreading, and wireless networks, we introduce the D-Temporal Multi-Broadcast (D-TMB) problem, which asks for scheduling the availability of edges so that a predetermined subset of sources reach all other vertices while optimizing the worst-case temporal distance D from any source. We show that D-TMB generalizes ReachFast (arXiv:2112.08797). We then characterize the computational complexity and approximability of D-TMB under six definitions of temporal distance D, namely Earliest-Arrival (EA), Latest-Departure (LD), Fastest-Time (FT), Shortest-Traveling (ST), Minimum-Hop (MH), and Minimum-Waiting (MW). For a single source, we show that D-TMB can be solved in polynomial time for EA and LD, while for the other temporal distances it is NP-hard and hard to approximate within a factor that depends on the adopted distance function. We give approximation algorithms for FT and MW. For multiple sources, if feasibility is not assumed a priori, the problem is inapproximable within any factor unless P = NP, even with just two sources. We complement this negative result by identifying structural conditions that guarantee tractability for EA and LD for any number of sources.

Problem

• Temporal Graphs
• Multi-Broadcast
• Temporal Distance
• Edge Scheduling
• Computational Complexity

Innovation

• Temporal Graphs
• Multi-Broadcast
• Temporal Distance
• Approximation Algorithms
• Computational Complexity