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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.
[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]
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.
Increased Code Size: Unrolling increases the number of instructions, leading to larger program binaries. Higher Storage Requirements: The expanded code takes up more memory, which can be problematic for microcontrollers or embedded systems with limited storage. Instruction Cache Pressure: The unrolled loop consumes more space in the instruction ...
If all are 1, then either the element is in the set, or the bits have by chance been set to 1 during the insertion of other elements, resulting in a false positive. In a simple Bloom filter, there is no way to distinguish between the two cases, but more advanced techniques can address this problem.
When we access a vertex v, the preferred path of the represented tree is changed to a path from the root R of the represented tree to the node v. If a node on the access path previously had a preferred child u, and the path now goes to child w, the old preferred edge is deleted (changed to a path-parent pointer), and the new path now goes ...
The problem of finding the best variable ordering is NP-hard. [16] For any constant c > 1 it is even NP-hard to compute a variable ordering resulting in an OBDD with a size that is at most c times larger than an optimal one. [17] However, there exist efficient heuristics to tackle the problem. [18]
Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical ...