Search results
Results from the WOW.Com Content Network
Since algorithms are platform-independent (i.e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system), there are additional significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.
In general, the output of these blocks cannot be used as the input unless it is captured by a register or state element which maintains its acyclic properties. [34] Electronic circuit schematics either on paper or in a database are a form of directed acyclic graphs using instances or components to form a directed reference to a lower level ...
Using the principle of inclusion–exclusion and Yates's algorithm for the fast zeta transform, k-colorability can be decided in time () [14] [16] [17] [18] for any k. Faster algorithms are known for 3- and 4-colorability, which can be decided in time () [19] and (), [20] respectively. Exponentially faster algorithms are also known for 5- and 6 ...
Figure 1. Finding the shortest path in a graph using optimal substructure; a straight line indicates a single edge; a wavy line indicates a shortest path between the two vertices it connects (among other paths, not shown, sharing the same two vertices); the bold line is the overall shortest path from start to goal.
Determining what typical input means is difficult, and often that average input has properties which make it difficult to characterise mathematically (consider, for instance, algorithms that are designed to operate on strings of text). Similarly, even when a sensible description of a particular "average case" (which will probably only be ...
Some basic properties include monotonicity and diagonal jump. [44] Persistent Betti numbers will be finite if is a compact and locally contractible subspace of . [45] Using a foliation method, the k-dim PBNs can be decomposed into a family of 1-dim PBNs by dimensionality deduction. [46]
If there is a polynomial-time algorithm for even one of them, then there is a polynomial-time algorithm for all the problems in NP. Because of this, and because dedicated research has failed to find a polynomial algorithm for any NP-complete problem, once a problem has been proven to be NP-complete, this is widely regarded as a sign that a ...
An algorithm solves if for every input such that there exists a satisfying (,), the algorithm produces one such . This is just another way of saying that f {\displaystyle f} is a function and the algorithm solves f ( x ) {\displaystyle f(x)} for all x ∈ Σ ∗ {\displaystyle x\in \Sigma ^{*}} .