Speaker: | Soham Chatterjee (TIFR) |
Organiser: | Kavitha Telikepalli |
Date: | Thursday, 24 Jul 2025, 15:00 to 16:00 |
Venue: | A-201 (STCS Seminar Room) |
In this talk we will show that the good Dijkstra's shortest path algorithm is universally optimal in both running time and number of comparisons when combined with a sufficiently efficient heap data structure namely Fibonacci Like priority queue with the working set property. We will prove that the working set property guarantees universal optimality for the problem of ordering vertices by their distance from the source vertex. The new heap data structure with working set property takes advantage of locality in heap operation which results in matching the optimal bounds of Fibonacci heaps but also provides the beyond-worst-case guarantee that the cost of extracting the minimum element is merely logarithmic in the number of elements inserted after it instead of logarithmic in the number of elements in the heap. This makes the extraction of recently added elements cheaper.