Till Tantau

This paper introduces logspace optimisation problems as

analogues of the well-studied polynomial-time optimisation

problems. Similarly to them, logspace

optimisation problems can have vastly different approximation

properties, even though the underlying existence and budget problems

have the same computational complexity. Numerous natural problems

are presented that exhibit such a varying ...
more >>>

Stasys Jukna, Georg Schnitger

We prove a general lower bound on the size of branching programs over any semiring of zero characteristic, including the (min,+) semiring. Using it, we show that the classical dynamic programming algorithm of Bellman, Ford and Moore for the shortest s-t path problem is optimal, if only Min and Sum ... more >>>

Meena Mahajan, Prajakta Nimbhorkar, Anuj Tawari

We study bounded depth $(\min, +)$ formulas computing the shortest path polynomial. For depth $2d$ with $d \geq 2$, we obtain lower bounds parametrized by certain fan-in restrictions on all $+$ gates except those at the bottom level. For depth $4$, in two regimes of the parameter, the bounds are ... more >>>

Kshitij Gajjar, Jaikumar Radhakrishnan

We construct a family of planar graphs $(G_n: n\geq 4)$, where $G_n$ has $n$ vertices including a source vertex $s$ and a sink vertex $t$, and edge weights that change linearly with a parameter $\lambda$ such that, as $\lambda$ increases, the cost of the shortest path from $s$ to $t$ ... more >>>