ECCC-Report TR18-049https://eccc.weizmann.ac.il/report/2018/049Comments and Revisions published for TR18-049en-usWed, 30 May 2018 18:20:17 +0300
Revision 1
| Greedy can beat pure dynamic programming |
Stasys Jukna,
Hannes Seiwert
https://eccc.weizmann.ac.il/report/2018/049#revision1Many dynamic programming algorithms for discrete 0-1 optimizationproblems are ``pure'' in that their recursion equations only use min/max and addition operations, and do not depend on actual input weights. 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 for this problem must perform $2^{\Omega(\sqrt{n})}$ operations. Since the greedy algorithm can also badly fail on some optimization problems, easily solvable by pure DP algorithms, our result shows that the computational powers of these two types of algorithms are incomparable.Wed, 30 May 2018 18:20:17 +0300https://eccc.weizmann.ac.il/report/2018/049#revision1
Paper TR18-049
| Greedy can also beat pure dynamic programming |
Stasys Jukna,
Hannes Seiwert
https://eccc.weizmann.ac.il/report/2018/049Many 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 for this problem must perform $2^{\Omega(n)}$ operations. Since the greedy algorithm can also badly fail on some optimization problems, easily solvable by pure DP algorithms, our result shows that the computational powers of these two types of algorithms are incomparable.Wed, 14 Mar 2018 19:21:36 +0200https://eccc.weizmann.ac.il/report/2018/049