Analysis of Algorithms - Homework 3 | CMSC 651, Assignments of Computer Science

Download Analysis of Algorithms - Homework 3 | CMSC 651 and more Assignments Computer Science in PDF only on Docsity! Fall 2006 CMSC 651: Homework 3 Due: Due Oct 11 and 12 (This is an ORAL HW.) 1. (50 points) We want to solve the Single source shortest path problem where all of the edges are positive integers that are ≤ C. In class we did this in O(V log C + E). Improve this. In particular, find an algorithm that is O((V log C)/ log log C+E). Use the ref Faster Algorithms for Shortest Path Problems by Ahuja, Mehlorn, Orlin, Tarjan which is posted on the course website. Your oral explanation must be very clear and you need to be able to answer questions about it. 2. (50 points) Consider the following alternative to the Path Compression UNION-FIND algo- rithm: When you do a FIND, instead of attaching every element encountered to the root, attach every element you find to its grandfather. Show that if the structure never gets more than n elements in it then m operations take O(m log∗ n). Use the ref A Potential-Based Amortized Analysis of the Union-Find Data Structure that is posted to the course website; Your oral explanation must be very clear and you need to be able to answer questions about it. 1