A Low Complexity based Edge Color Matching Algorithm for Regular Bipartite Multigraph
نویسندگان
چکیده
An edge coloring of a graph G is a process of assigning colors to the adjacent edges so that the adjacent edges represents the different colors. In this paper, an algorithm is proposed to find the perfect color matching of the regular bipartite multigraph with low time complexity. For that, the proposed algorithm is divided into two procedures. In the first procedure, the possible circuits and bad edges are extracted from the regular bipartite graph. In the second procedure, the bad edges are rearranged to obtain the perfect color matching. The depth first search (DFS) algorithm is used in this paper for traversing the bipartite vertices to find the closed path, open path, incomplete components, and bad edges. By the proposed algorithm, the proper edge coloring of D – regular bipartite multi-graph can be obtained in O (D.V) time. Keywords—matching; edge-coloring; complexity; bipartite multigraph; DFS
منابع مشابه
An Algorithm for Computing Edge Colorings on Regular Bipartite Multigraphs
In this paper, we consider the problem of finding an edge coloring of a d-regular bipartite multigraph with 2n vertices and m = nd edges. The best known deterministic algorithm (by Cole, Ost, and Schirra) takes O(m log d) time to find an edge coloring of such a graph. This bound is achieved by combining an O(m)-time perfect-matching algorithm with the Euler partition algorithm. The O(m) time bo...
متن کاملExcessive factorizations of bipartite multigraphs
Let G be a multigraph. We say that G is 1-extendable if every edge of G is contained in a 1-factor. Suppose G is 1-extendable. An excessive factorization of G is a set F = {F1, F2, . . . , Fr} of 1-factors of G whose union is E(G) and, subject to this condition, r is minimum. The integer r is called the excessive index of G and denoted by χ′e(G). Analogously, let m be a positive integer. We say...
متن کاملSwitch Scheduling via Randomized Edge Coloring
The essence of an Internet router is an n n switch which routes packets from input to output ports. Such a switch can be viewed as a bipartite graph with the input and output ports as the two vertex sets. Packets arriving at input port i and destined for output port j can be modeled as an edge from i to j. Current switch scheduling algorithms view the routing of packets at each time step as a s...
متن کاملA simple algorithm for edge-coloring bipartite multigraphs
It is well known that the chromatic index of any bipartite multigraph G with n vertices and m edges is equal to its maximum degree k. The best algorithm currently known for finding a proper k-edge-coloring of such a multigraph runs in time O(m log k), see [2], or the forthcoming book [6], and applies rather elaborate data structures together with the basic approach of [5]. Another algorithm, of...
متن کاملFeasible edge colorings of trees with cardinality constraints
A variation of preemptive open shop scheduling corresponds to nding a feasible edge coloring in a bipartite multigraph with some requirements on the size of the di erent color classes. We show that for trees with xed maximum degree, one can nd in polynomial time an edge k-coloring where for i = 1; : : : ; k the number of edges of color i is exactly a given number hi, and each edge e gets its co...
متن کامل