TSP is a difficult problem. Multi-TSP is probably much worse. I’m not sure you can find good solutions with ad-hoc methods like this. Have you tried meta-heuristic methods ? I’d try using the Cross Entropy method first : it shouldn’t be too hard to use it for your problem. Otherwise look for Generic Algorithms, Ant … Read more
O( n log n ) solution
Pedro Moreno and others at Google/Youtube work on it. They use finite-state transducers to recognize sequences of music phone units, similar to phonemes in automatic speech recognition. Check out this article: Eugene Weinstein, Pedro J. Moreno; Music Identification with Weighted Finite-State Transducers, Proceedings of the International Conference in Acoustics, Speech and Signal Processing (ICASSP), 2007. … Read more
One possibility is to compute the lexicographically least topological order. The algorithm is to maintain a priority queue containing the nodes whose effective in-degree (over nodes not yet processed) is zero. Repeatedly dequeue the node with the least label, append it to the order, decrement the effective in-degrees of its successors, enqueue the ones that … Read more
The pseudocode that you’ve posted will correctly balance a tree. That said, it is too inefficient to be practical – notice that you’re recursively exploring the entire tree trying to do rebalancing operations, which will make all insertions and deletions take O(n) time, eating away all the efficiency gains of having a balanced tree. The … Read more
I think you can solve this using the dynamic programming longest increasing subsequence algorithm: http://www.algorithmist.com/index.php/Longest_Increasing_Subsequence Accounting for the rotations is easy enough: for every tower all you have to check is what happens if you use its height as the length of the base and its width as the height and what happens if you … Read more
Kruskal is O(E log E); your derivation is right. You could also say O(E log V) because E <= V * V, so log(E) <= 2 log(V) (I don’t know why I remember that, other than that I think a prof put that on an exam at one point…)
I am one of the developer that works on the scheduler part of a student information system. During our original approach of the scheduling problem, we researched genetic algorithms to solve constraint satisfaction problems, and even though we were successful initially, we realized that there was a less complicated solution to the problem (after attending … Read more
Obvious answers would be: Sort both lists, then check each element to see if they’re identical Add the items from one array to a hashtable, then iterate through the other array, checking that each item is in the hash nickf’s iterative search algorithm Which one you’d use would depend on whether you can sort the … Read more
It’s NP-hard Some bad news: This problem is NP-hard, so unless P=NP, there is no algorithm that can efficiently solve all instances of it. I’ll prove this by showing how to convert, in polynomial time, any given instance of the NP-hard problem 3SAT into a dependency graph structure suitable for input to your problem, and … Read more