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Irrespective of the problem category, the process of solving a problem can be divided into two broad steps: constructing an efficient algorithm, and implementing the algorithm in a suitable programming language (the set of programming languages allowed varies from contest to contest). These are the two most commonly tested skills in programming ...
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. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
The problem of computing longest common subsequences is a classic computer science problem, the basis of data comparison programs such as the diff utility, and has applications in computational linguistics and bioinformatics.
Interval scheduling is a class of problems in computer science, particularly in the area of algorithm design. The problems consider a set of tasks. Each task is represented by an interval describing the time in which it needs to be processed by some machine (or, equivalently, scheduled on some resource). For instance, task A might run from 2:00 ...
This problem was given the name the Two Generals Paradox by Jim Gray [8] in 1978 in "Notes on Data Base Operating Systems" [9] starting on page 465. This reference is widely given as a source for the definition of the problem and the impossibility proof, though both were published previously as mentioned above.
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.
UNIQUE SAT [22] is the problem of determining whether a formula has exactly one assignment. It is complete for US, [23] the complexity class describing problems solvable by a non-deterministic polynomial time Turing machine that accepts when there is exactly one nondeterministic accepting path and rejects otherwise.