A K-Main Routes Approach to Spatial Network Activity Summarization(SNAS) Group 8
Outline Motivation Key Concepts Problem Statement Challenges Related Work Contributions Algorithm Validation Assumption and Future Work
Motivation Pedestrian Fatalities Crime Activities
Key Concepts Activity Set Summary Path Activity Coverage Active Edge, Active Node, Inactive Node Active Node Ratio
Problem Statement Given: A spatial network G = (N, E) with weight function w(u, v) ≥ 0 for each edge A set of activities and their locations A desired number of summary paths, called K Find: A summary path set of size K, called P A partitioning of activities across these summary paths Objective: Maximize the activity coverage of each summary path for the group it represents. Constraints: Each summary path is a shortest path between its end-nodes.
Challenges Computational Complexity SNAS is computationally challenging because of the large number of K subsets of shortest paths in a spatial network. If disjoint paths ? Less computation If overlapping paths ? NP-complete Problem
Related Work Previous work has focused on either geometry or subgraph-based approaches (only one path), and cannot summarize activities using multiple paths. Geometry-based K-means Network-Based Variable-Distance Clumping Method (NT-VCM)
Contributions It shows that SNAS is NP-complete. It proposes new techniques for improving the performance of K Main Routes: Network Voronoi activity Assignment and Divide and conquer Summary Path Re-computation. Their correctness are demonstrated. The computation cost of KMR can be calculated. It presents a case study comparing KMR with geometry-based summarization techniques on pedestrian fatality data. It tests the performance and scalability of KMR using both synthetic and real world data sets and demonstrates the computational efficiency of the performance-tuning strategies.
K-Main Routes (KMR) Algorithm Select K paths as initial summary paths Repeat: Phase 1 Form K clusters by assigning each activity to its closest summary path Phase 2 Re-compute summary path of each cluster When summary paths do not change, terminate. Using performance-tuning decisions: Inactive node pruning 1 Network Voronoi Activity assignment (NOVA_TKDE) 2 Divide and Conquer Summary Path Re-computation (D-SPAE_TKDE)
K-Main Routes (KMR) Algorithm
Validation Use the real and synthetic data Compare and optimize the computational cost in performance- tuning decisions such as Network Voronoi Activity assignment and Divide and Conquer Summary Path Re-computation Observe the trends about number of nodes, routes, activities and active node ratio on seven versions of KMR Use one case study – Orlando Crime stat
Effect of Number of Nodes Computational savings increase as the number of nodes Real data Number of routes K= 30 Number of activities = 602 for nodes Active node ratio = 0.07 Synthetic data Number of routes K= 2 Number of activities =1200 Active node ratio = 0.2
Effect of the Number of Routes Computational savings increase as the number of routes Real data Number of nodes = Number of activities = 369 Active node ratio = Synthetic data Number of nodes = 1000 Number of activities =1200 Active node ratio = 0.2
Effect of the Number of Activities and Active Node Ratio Computational savings increase with number of activities and active node ratio. Synthetic data Number of nodes = 1000 Number of routes K= 2 Number of activities =1200 Active node ratio = 0.2
Case Study
Assumption and Further Work The performance which activities are around the nodes Handle the accidents in height (overpass) Can be applied to more domains (disaster) Distance based instead of coverage based The accidents from static to dynamic Overlapping paths