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The Kemeny–Young method is an electoral system that uses ranked ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.
In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002. [1] [2] [3] The conjecture postulates that the problem of determining the approximate value of a certain type of game, known as a unique game, has NP-hard computational complexity.
Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem [3]: SP13 Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric.
A problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC.
As both n and L grow large, SSP is NP-hard. The complexity of the best known algorithms is exponential in the smaller of the two parameters n and L. The problem is NP-hard even when all input integers are positive (and the target-sum T is a part of the input). This can be proved by a direct reduction from 3SAT. [2]
If P were in fact equal to NP, then a polynomial-time algorithm would exist for solving NP-complete, and by corollary, all NP problems. [4] The complexity class NP is related to the complexity class co-NP, for which the answer "no" can be verified in polynomial time. Whether or not NP = co-NP is another outstanding question in complexity theory ...
Cocktail shaker sort or bidirectional bubble sort, a bubble sort traversing the list alternately from front to back and back to front; Comb sort; Gnome sort; Odd–even sort; Quicksort: divide list into two, with all items on the first list coming before all items on the second list.; then sort the two lists. Often the method of choice
To find a maximum clique, one can systematically inspect all subsets, but this sort of brute-force search is too time-consuming to be practical for networks comprising more than a few dozen vertices. Although no polynomial time algorithm is known for this problem, more efficient algorithms than the brute-force search are known.