SERVING THE QUANTITATIVE FINANCE COMMUNITY

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Where do you end up if you do the opposite of what your navigator tells you to do?

Fun problem! A few requirements.....1. No dead-end streets (traps the driver)2. No one-way streets (forces the driver to follow the instructions)3. A spherically symmetric network and set of destination (every address has an antipodal address)4. No N-way intersections with N>3 (creates ambiguity: instructions say "straight" but "right" and "left" are possible)(note: if one has already taken 1 or more opposite directions, then "reverse" is actually a route back to the avoided destination and must never be taken)Note: there's more constraints if one wants to ensure that the point of indifference (where the GPS instructions flip from telling you to go back to telling you to go forward) is antipodal and unique.
Last edited by Traden4Alpha on October 3rd, 2015, 10:00 pm, edited 1 time in total.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Where do you end up if you do the opposite of what your navigator tells you to do?

P.S. The answer to your unintended question is "sometimes dead". About once or twice a year in the U.S. someone follows their GPS navigator instructions onto a shortcut through impassible mountain or desert roads with tragic results.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Where do you end up if you do the opposite of what your navigator tells you to do?

Good mod to rule 4 and interesting issue with D-to-B vs. D*-to-BThe hypercube issue illustrates another restriction:5. No loops that don't include great circle loops.Driving in Iceland, one would soon come to the point on the main loop road highway where forward and backward are equidistant to the avoided destination and one is still quite far from the antipode of the destination.If the destination happens to be a hub in the road network, then the antipodal point of the hub may not be reachable without going through the hub. This is a generalization of the dead-end rule in which one starts in a dead-end branch or dead-end tree of the graph and both the destination and the antipode of the destination requiring driving out of that dead-end. So, "NO TREES" in the road network topology is a generalization of requirement #1.P.S. We forgot rule #0: total connectivity: every starting point is connected to every destinatiion and it's antipode. (no oceans)

Cuchulainn
Posts: 61185
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Where do you end up if you do the opposite of what your navigator tells you to do?

Tom Tom doesn't work in Italy..
http://www.datasimfinancial.com
http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself
Jean Piaget

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Where do you end up if you do the opposite of what your navigator tells you to do?

QuoteOriginally posted by: CuchulainnTom Tom doesn't work in Italy..Perhaps doing the opposite of Tom Tom (Mot Mot) would help.

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...

 JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...

GZIP: On