# A Framework of Vehicle Usage Optimization for Tour Purposes
## 2 Related Research
They also developed a private filter to ascertain the actual GNN while ensuring that user locations remain undisclosed to all parties, including the LSP. They also proposed an efficient algorithm for evaluating GNN queries involving imprecise locations. They demonstrated the effectiveness of the proposed technique through an extensive experimental study. Ref. [16] discusses a new type of query in Spatial Databases called the Trip Planning Query (TPQ). TPQ retrieves the best trip that starts at a given starting point, passes through at least one point from each category of points of interest in space, and ends at a given destination. The paper presents fast approximation algorithms for TPQ in a metric space, addressing the difficulty of the query due to the multiple choices per category. The approximation algorithms have varying ratios that depend on the number of types, the maximum number of points per category, or both, and all of them run in polynomial time. The paper introduces efficient heuristics for managing large datasets stored in external memory, utilizing several proposed algorithms. The paper introduces efficient heuristics for managing large datasets stored in external memory, utilizing several proposed algorithms. Ref. [17] presents a novel spatial-social optimization problem, Optimal Group Route, for multi-user itinerary planning in location-based applications. The problem formulation lets users specify individual sources, destinations, preferences on Point-of-Interest (POI) categories, and distance constraints. The goal is to find an itinerary that can be traversed by all users while maximizing the group's preference of POI categories in the itinerary,considering the agreement and disagreement among group members. The article proposes two efficient greedy algorithms with bounded approximation ratios, an exact solution that computes the optimal itinerary by exploring a limited number of paths in the road network, and a scaled approximation algorithm to speed up the dynamic programming employed by the exact solution. The researchers assess the proposed solutions using two real-world road network/POI datasets, and the results confirm their effectiveness and efficiency. The article contributes to advancing existing group trip planning studies by maximizing the group's social experience. Ref. [18] proposed a new type of trip planning query, called Subgroup Trip Planning (SGTP) query, which allows a group to identify the subgroup and points of interest (POIs) from each required type (e.g., restaurant, shopping center, and movie theater) that have the minimum aggregate trip distance for any subgroup size. The authors highlighted that the computation of POI sets for all possible subgroups using group trip planning (GTP) algorithms is relatively inexpensive. Therefore, the authors proposed an algorithm to compute answers for different subgroup sizes concurrently with less query processing overhead. The authors focused on minimizing the subgroup's total and maximum trip distance. The researchers assessed the proposed algorithms using both real and synthetic datasets, and the experiments demonstrated their efficiency. In Ref. [19], the authors discussed the growth of location-based social networks and the emergence of a new query type called group trip planning (GTP) query. GTP query involves a group of individuals trying to minimize the total travel distance for all members when planning a trip to different locations, such as a restaurant and a movie theater. The passage also notes the development of efficient algorithms for addressing GTP queries, which the researchers tested through extensive experiments. In Ref. [20], the authors discussed how they integrated social networks and spatial road networks to form a spatial-social network, offering potential applications such as trip recommendations.