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Open problems around exact algorithms by Gerhard J. Woeginger, Discrete Applied Mathematics 156 (2008) 397–405. The RTA list of open problems – open problems in rewriting. The TLCA List of Open Problems – open problems in area typed lambda calculus
In its second phase, the simplex algorithm crawls along the edges of the polytope until it finally reaches an optimum vertex.The criss-cross algorithm considers bases that are not associated with vertices, so that some iterates can be in the interior of the feasible region, like interior-point algorithms; the criss-cross algorithm can also have infeasible iterates outside the feasible region.
The circuit on the left is satisfiable but the circuit on the right is not. In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true. [1]
A complete problem for a given complexity class C and reduction ≤ is a problem P that belongs to C, such that every problem A in C has a reduction A ≤ P. For instance, a problem is NP -complete if it belongs to NP and all problems in NP have polynomial-time many-one reductions to it.
In the worst case, the algorithm results in a tour that is much longer than the optimal tour. To be precise, for every constant r there is an instance of the traveling salesman problem such that the length of the tour computed by the nearest neighbour algorithm is greater than r times the length of the optimal tour. Moreover, for each number of ...
Additionally, verifiers require a potential solution known as a certificate, c. For the Hamiltonian Path problem, c would consist of a string of vertices where the first vertex is the start of the proposed path and the last is the end. [22] The algorithm will determine if c is a valid Hamiltonian Path in G and if so, accept.
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
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables , which is solved by constraint satisfaction methods.