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math.PR2018
When Does Hillclimbing Fail on Monotone Functions: An entropy compression argument
Johannes Lengler, Anders Martinsson, Angelika Steger
Hillclimbing is an essential part of any optimization algorithm. An important benchmark for hillclimbing algorithms on pseudo-Boolean functions are (s…
math.PR2018
The "No Justice in the Universe" phenomenon: why honesty of effort may not be rewarded in tournaments
Peter Hegarty, Anders Martinsson, Edvin Wedin
In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pai…
math.PR2016
Shotgun edge assembly of random jigsaw puzzles
Anders Martinsson
In recent work by Mossel and Ross, it was asked how large has to be for a random jigsaw puzzle with different shapes of "jigs" to have exactly one solution. The jigs are as…