April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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Additional Exercises with Solutions 735
12. Prove that the following relationships hold between complexity classes.
(i) LOGTIME ⊆ LOGSPACE
(ii) LOGSPACE ⊆ PTIME
(iii) PTIME ⊆ PSPACE
(iv) NPTIME ⊆ PSPACE
(v) NPSPACE ⊆ EXPTIME
13. If we replace the assignment X ← 3X + 1 by X ← 2X + 1 in the 3X + 1 program given in the text, will it
halt for every positive integer?
14. Show that an algorithm that makes atmost constant number of calls to polynomial time subroutines runs
in polynomial time, but that a polynomial number of calls to polynomial time subroutines may result in
an exponential time algorithm.
15. Show that P ⊆ Co-NP.
16. Show that if NP ≠ Co-NP, then P ≠ NP.
E.1.10 Chapter 18: Some NP and NPC Problems
1. (Vertex cover) The problem ...
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