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REPORTS > KEYWORD > SHORTEST PATH:
Reports tagged with shortest path:
TR03-077 | 4th September 2003
Till Tantau

Logspace Optimisation Problems and their Approximation Properties

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 >>>


TR15-127 | 7th August 2015
Stasys Jukna, Georg Schnitger

On the Optimality of Bellman--Ford--Moore Shortest Path Algorithm

Revisions: 1

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 >>>


TR18-146 | 18th August 2018
Meena Mahajan, Prajakta Nimbhorkar, Anuj Tawari

Shortest path length with bounded-alternation $(\min, +)$ formulas

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 >>>


TR18-211 | 3rd December 2018
Kshitij Gajjar, Jaikumar Radhakrishnan

Parametric Shortest Paths in Planar Graphs

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 >>>




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