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Spread and Page Rank for Interactive Maps
This document proposes a new algorithm called Spread and PageRank to determine which airports to display on interactive maps at different zoom levels. It combines two metrics: PageRank, which measures an airport's connectivity to other important airports, and Spread, which measures the distance to the nearest airport of higher rank. This avoids having airports bunch together or leave large empty spaces. The algorithm pre-calculates PageRank and Spread for all airports, then displays the top N airports at each zoom level based on the product of their Rank and Spread scores. This flexible approach can be applied beyond airports to display various map objects in a spaced-out manner based on both connectivity and coverage area.
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Spread and Page Rank for Interactive Maps
- 1. Spread and PageRank for Interactive Maps Wm Leler - Flightstats, Inc. wm@flightstats.com
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- 3. openstreetmap.org Missing: San Francisco,San Jose, Los Angeles, LasVegas, Phoenix, Seattle,Vancouver, Detroit, Dallas, NYC, Miami
- 4. Stamen Terrain Beaverton? Hillsboro?Forest Grove? Tigard?
- 5. Google Maps Seattle? Denver?Salt Lake City? LasVegas?
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- 7. The Big Problem •A map is a spatial display of a bunch of objects: cities, highways, parks, airports, etc. • At most zoom levels, there are far too many objects to display. • What is the best way to pick which objects to display (per zoom level) on a map?
- 8. Our Immediate Problem • AtFlightStats we need to decide which airports to draw on a map Every airport that supplies us with flight data (4180)
- 9. FAA Categories Based on% of passenger-enplanements 1. Primary large hub (>1% of p-e) 2. Primary medium hub (.25 - 1%) 3. Primary small hub (.05 - .25%) 4. Primary non-hub (<0.05%) 5. Secondary (< 10,000 p-e / year)
- 10. Bad Solution • Notso good for maps • Airports bunch together and leave big empty spaces Bunching Empty Spaces Bunching Delay Map
- 11. • South Americahas only 3 large primary airports • Two serve the same city (Rio) • Africa has one (JNB) Even Worse Internationally
- 12. • Should bedependent on zoom level • as you zoom in, you want to see more • Number of passengers is a bad measure • short commuter flights to little airports should count less • flights to other major airports should count more More Problems
- 13. Goals • Show “important”airports • major airports • plus less major airports if they are the primary airport for an area • Avoid airports “bunching up”
- 14. Solution Importance of anairport is based on: 1. How connected it is to other airports weighted by the importance of each other airport (recursive) 2. Area for which it is the primary airport 3. Based on current map view
- 15. Connectivity • Calculate connectivityusing the PageRank algorithm (by Larry Page at Google, adapted by Steve Wilson at FlightStats) SEA PDX EUG PDT RDM PR(PDX) = foreach airport x: flights(PDX, x) * PR(x)
- 16. Connectivity • Calculate connectivityusing the PageRank algorithm (by Larry Page at Google, adapted by Steve Wilson at FlightStats) SEA PDX EUG PDT RDM PR(PDX) = foreach airport x: flights(PDX, x) * PR(x) .0025 .0036 .00014 .0002.0003
- 17. Spread • (Page) Rankstill suffers from bunching and empty spaces • Add Spread – the distance to the closest airport of higher rank • a reasonable proxy for the area • The Spread for PDX is 111.98 nautical miles (the distance to SEA)
- 18. Combining Rank and Spread RankSpread X SFO 0.0040 293.5 1.19 OAK 0.0015 10.26 0.0158 SJC 0.0012 24.8 0.0287 SMF 0.0011 65.6 0.0702 The four biggest airports in Northern CA
- 19. Algorithm 1. Pre-calculate Rankand Spread for all airports (they don’t change very often) 2. For each map view, display the N airports with the largest product of Rank and Spread 3. (optionally) set minimum Rank and Spread
- 20. Flexibility • Applications canpick their weighting of Rank and Spread, and value of N • N can depend on zoom level • Can also use them as limits • minimum Spread to debunch airports • minimum Rank to hide small airports
- 21. Beyond Airports • Canuse Spread to space out almost anything on a map • cities, neighborhoods, roads, parks, mountains, rivers, lakes, ... • your data! • Rank emphasizes connectivity over raw size or category
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