I am trying to implement the nearest insertion TSP heuristic. However, I am wondering if it matters which node I insert into the subgraph first. For example, should I start with one node; calculate the distance between this node and the other nodes; and sort the other nodes by this distance? Then, I will insert … Read more
I know the Floyd-Warshall, and I also clearly understand the proof of running time of $O(V^3)$ of F-W algorithm. However, consider this algorithm: Let $dp[i][j][n]$ denote the shortest path from $V_i$ to $V_j$ using at most $n$ vertices. Use $dp[i][j][n] = \min_{V_k\text{ adjacent to } V_i} (e_{ik}+dp[k][j][n-1], dp[i][j][n-1])$ to compute all values of $dp[i][j][n]$. This … Read more
Given a set of points in the 2-d plane, find the minimum edge size, L, that would allow the construction of a tree whose edges connect all given points, but no edge exceeds length L. Here is an algorithm, which I think might work but seems slow: Pick a random point find the distance of … Read more
Given a graph with positive edge weight representing “time to travel through”, and 2 or more pairs of start/end vertices, we can find concurrent paths for the pairs such that the maximum cumulative weight along any path is minimum, using classic shortest path algorithms. Now what if the weight is not static, but represents “congestion … Read more
I am trying to write a general purpose locking algorithm which allows me to lock a range of contiguous values in a sorted array. To start with, these could be exclusive locks – so two concurrent locks must be non-overlapping. What could be a good, scalable algorithm to do this? (Scalable ~ concurrent) A specific … Read more
In a language supporting CPS, but no built in global state, we can represent a state based computation using a function. We call this function a state function. Assume the function takes three arguments, get, put, and cont. The intended interpretation of these functions is that get takes a continuation, and applies that continuation to … Read more
Let’s say we have a simple connected and undirected graph G(V,E). The game is played with two players. For each game, player A starts at a node t, and player B at a node v. There is also a node d which is the same for every game. In the game, player A always plays … Read more
Assume that we have an anti-symmetric matrix that consists of 1’s and -1’s and 0’s. All the elements of the main diagonal are 0 and each row and each column has exactly one 1, and one -1. Design an algorithm that replaces all 1’s with -1’s and vice versa only by swapping some rows and … Read more
I’m reading about the algorithm of finding the ranks of all points in a 2D plane, I don’t understand the time complexity formula for it. It has four steps: Compute the median of x-coordinates of all point, and divide the plane into two half Left, and Right. Recursively do 1. then when there is only … Read more
Consider these two equation. m1+m2+m3+m4=Mm|m1|+|m2|+|m3|+|m4|=Nm where {mi,Mm,Nm}∈Z. Given the value of (Nm,Mm) we can find the different solutions for (m1,m2,m3,m4). The solutions are ordered in a particular way which is best explained by giving a few examples. For e.g. with (Nm=2,Mm=2) the solutions are {{0, 0, 0, 2}, {0, 0, 1, 1}, {0, 0, 2, … Read more
