euler tour造句

• To address this problem, we make use of an algorithm called prefix sum by using the Euler tour technique.
• Their data structure uses an Euler tour technique to transform the input tree into a sequence and then finds range minima in the resulting sequence.
• With the Euler tour technique, a tree could be represented in a flat style, and thus prefix sum could be applied to an arbitrary tree in this format.
• Make the input multigraph Eulerian by adding a new vertex connected by an edge to every odd-degree vertex, find an Euler tour, and choose an orientation for the tour.
• If a connected graph is 2 " k "-regular and has an even number of edges it may also be " k "-factored, by choosing each of the two factors to be an alternating subset of the edges of an Euler tour.
• Doubling the edges of a " T "-join causes the given graph to become an Eulerian multigraph ( a connected graph in which every vertex has even degree ), from which it follows that it has an Euler tour, a tour that visits each edge of the multigraph exactly once.
• When " k " is an odd number, A path or cycle with \ tbinom { k } { 2 } edges has an exact coloring, obtained by forming an exact coloring of the complete graph " K " " k " and then finding an Euler tour of this complete graph.
• This representation allows us to quickly answer the question " what is the root of node v ? " by just moving to the first node of the ET tree ( since nodes in the ET tree are keyed by their location in the Euler tour, and the root is the first and last node in the tour ).
• Their method involves forming an Euler tour of a graph formed from the input tree by doubling every edge, and using this tour to write a sequence of level numbers of the nodes in the order the tour visits them; a lowest common ancestor query can then be transformed into a query that seeks the minimum value occurring within some subinterval of this sequence of numbers.
• In the same paper, Karloff and Shmoys also present a linear time algorithm for coloring multigraphs of maximum degree three with four colors ( matching both Shannon's and Vizing's bounds ) that operates on similar principles : their algorithm adds a new vertex to make the graph Eulerian, finds an Euler tour, and then chooses alternating sets of edges on the tour to split the graph into two subgraphs of maximum degree two.
• The sequence resulting from this transformation has a special form ( adjacent numbers, representing heights of adjacent nodes in the tree, differ by ? ) which they take advantage of in their data structure; to solve the range minimization problem for sequences that do not have this special form, they use Cartesian trees to transform the range minimization problem into a lowest common ancestor problem, and then apply the Euler tour technique to transform the problem again into one of range minimization for sequences with this special form.