Salesforce is optimizing its field service management system to improve customer satisfaction. Field service agents are tasked with visiting multiple client locations to complete service requests. Each client location is represented as a node in the city's service map, and roads between locations are represented as edges with travel times. The system must calculate the minimum time required for a field service agent to: 1. Start at the headquarters (HQ) located at node 0. 2. Visit all client locations (represented by k distinct nodes) in any sequence to complete their service requests. 3. Return to the headquarters (node 0) after completing all visits. The city's infrastructure is represented as a graph comprising of n connection_nodes junctions and m bidirectional roads that interconnect them. Each road, which links cities connection_from[i] and connection_to[i], has an associated connection_cost[i] that represents the time required to travel along the road. Determine the minimum time required to accomplish this task.