Radu Mariescu-Istodor Winning the game Playing strategies for O-Mopsi Lahari Sengupta Radu Mariescu-Istodor Pasi Fränti 31.12.2015

What is O-Mopsi?

Classical orienteering Devices: Map and compass Targets brought to nature for the event Motivation: Orienteering is difficult to create and maintain. Easier with O-Mopsi. Control points may be lost. Targets might become outdated in O-Mopsi. Not everyone can play the game at 17:00. In O-Mopsi you can play at any time. Disadvantages: Battery, Weather, Find all controls In pre-defined order Fastest wins 3

Mopsi orienteering (O-Mopsi) Smartphone and GPS Targets real objects Pictures of targets Find all controls In free order Fastest wins

Challenges of playing ? Orienteering: Knowing your location Optimizing paths to targets O-Mopsi: Finding best order Optimizing paths to targets ?

Winning the game

What matters Order of visiting targets Where to start playing Travelling salesman problem (TSP) Human strategies: nearest neighbor, clustering Computer strategies: optimal, optimization Where to start playing Remove longest edge from TSP? Blind selection Comparison of various heuristics Navigating to targets Effects of routing

Order of targets

Algorithmic problem Minimize total distance With N targets there are N! possible orders Variant of travelling salesman problem (TSP) 478 m 280 m 250 m 250 m 228 m 30 m

How much it matters? ? 5 km 4 km Nearest target strategy Optimal order 3 2 More targets, harder to solve Nearest neighbor strategy XX% longer than optimal (average) Lahari: - Some calculations of distances of SciFest 2014 easy (min,max,median) - Algorithm variations with Helsinki - Overall, with the function of number of targets and complexity 1 5 km Optimal order 3 ? 2 4 km 1

Effect of starting point

Where to start? Targets not visible before start (if known, can start at one target) No time for planning route (Time starts when game opens) Game area (bounding box) shown Start must be chosen blindly Need two pics: Before start After start Need to implement TSP with user-selected start point!

Start point strategy 1 Center of the area x,x km Center ?

Start point strategy 2 Corner of the area x,x km ?

Start point strategy 3 Somewhere at the shorter edge x,x km ? Short edge

Likely direction of optimal route Start point matters Every side has at least one target Optimal order likely to go along longer side (rather than random zig zag) Heuristic: Start from the shorter side Likely direction of optimal route xmax ymax Longer side Start Shorter side xmin ymin

Start point statistics according to target location Optimal start point located: First/last target along the short side: xx % First/last target along the long side: xx % Some other target: xx %

Start point statistics according to grid Calculate optimal tour Divide the area into 20%20% grid Locate the start and end points of the tour in the grid Longer side Shorter side

Road network

Effect of route network Bird distance vs. roads Buildings and small housing in city area Real distance xx-yy % longer than bird’s distance Can also affect the order of the targets Bird distance Routing 417 m 753 m

Effect of route network Start point changes Bird distance Routing 13.4 km 21.4 km

River has big impact 2.1 km 3.8 km Bird distance Routing crossing

Effect of transport mode Shorter routing by walk Routing by car

Limitations of routing Limitations in street crossing No shortcuts No routes via open plaza