All reports by Author Hannes Seiwert:

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TR20-178
| 30th November 2020
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Stasys Jukna, Hannes Seiwert, Igor Sergeev#### Reciprocal Inputs in Arithmetic and Tropical Circuits

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TR18-127
| 9th July 2018
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Stasys Jukna, Hannes Seiwert#### Approximation Limitations of Tropical Circuits

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TR18-049
| 14th March 2018
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Stasys Jukna, Hannes Seiwert#### Greedy can also beat pure dynamic programming

Revisions: 1

Stasys Jukna, Hannes Seiwert, Igor Sergeev

It is known that the size of monotone arithmetic $(+,\ast)$ circuits can be exponentially decreased by allowing just one division "at the very end," at the output gate. A natural question is: can the size of $(+,\ast)$ circuits be substantially reduced if we allow divisions "at the very beginning," that ... more >>>

Stasys Jukna, Hannes Seiwert

We develop general lower bound arguments for approximating tropical

(min,+) and (max,+) circuits, and use them to prove the

first non-trivial, even super-polynomial, lower bounds on the size

of such circuits approximating some explicit optimization

problems. In particular, these bounds show that the approximation

powers of pure dynamic programming algorithms ...
more >>>

Stasys Jukna, Hannes Seiwert

Many dynamic programming algorithms are ``pure'' in that they only use min or max and addition operations in their recursion equations. The well known greedy algorithm of Kruskal solves the minimum weight spanning tree problem on $n$-vertex graphs using only $O(n^2\log n)$ operations. We prove that any pure DP algorithm ... more >>>