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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.
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 ...
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.
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 ...
For example, enforcing arc consistency on binary acyclic problems allows for telling whether the problem is satisfiable. Enforcing strong directional i {\displaystyle i} -consistency allows telling the satisfiability of problems that have induced width i − 1 {\displaystyle i-1} according to the same order.
The following example demonstrates dynamic loop unrolling for a simple program written in C. Unlike the assembler example above, pointer/index arithmetic is still generated by the compiler in this example because a variable (i) is still used to address the array element.
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] In weighted complete graphs with non-negative edge weights, the weighted longest path problem is the same as the Travelling salesman path problem, because the longest path always includes all ...
In computer science, a trie (/ ˈ t r aɪ /, / ˈ t r iː /), also known as a digital tree or prefix tree, [1] is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key.