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The k shortest path routing problem is a generalization of the shortest path routing problem in a given network. It asks not only about a shortest path but also about next k−1 shortest paths (which may be longer than the shortest path). A variation of the problem is the loopless k shortest paths.
Problem 2. Find the path of minimum total length between two given nodes P and Q. We use the fact that, if R is a node on the minimal path from P to Q, knowledge of the latter implies the knowledge of the minimal path from P to R. is a paraphrasing of Bellman's Principle of Optimality in the context of the shortest path problem.
Maximum lengths of snakes (L s) and coils (L c) in the snakes-in-the-box problem for dimensions n from 1 to 4. The problem of finding the longest path or cycle that is an induced subgraph of a given hypercube graph is known as the snake-in-the-box problem. Szymanski's conjecture concerns the suitability of a hypercube as a network topology for ...
Two octads intersect (have 1's in common) in 0, 2, or 4 coordinates in the binary vector representation (these are the possible intersection sizes in the subset representation). An octad and a dodecad intersect at 2, 4, or 6 coordinates. Up to relabeling coordinates, W is unique. The binary Golay code, G 23 is a perfect code. That is, the ...
The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc. For example, a binary string of eight bits (which is also called a byte) can represent any of 256 possible values and can, therefore, represent a wide variety ...
[9]: 52 With insertion as the code below shows, the adequate rotation immediately perfectly rebalances the tree. In figure 1, by inserting the new node Z as a child of node X the height of that subtree Z increases from 0 to 1. Invariant of the retracing loop for an insertion. The height of the subtree rooted by Z has increased by 1.
An object code optimizer, sometimes also known as a post pass optimizer or, for small sections of code, peephole optimizer, forms part of a software compiler. It takes the output from the source language compile step - the object code or binary file - and tries to replace identifiable sections of the code with replacement code that is more ...
[1] If the longest path problem could be solved in polynomial time, it could be used to solve this decision problem, by finding a longest path and then comparing its length to the number k. Therefore, the longest path problem is NP-hard. The question "does there exist a simple path in a given graph with at least k edges" is NP-complete. [2]