منابع مشابه
On Random Greedy Triangle Packing
The behaviour of the random greedy algorithm for constructing a maximal packing of edgedisjoint triangles on n points (a maximal partial triple system) is analysed with particular emphasis on the final number of unused edges. It is shown that this number is at most n, “halfway” from the previous best-known upper bound o(n) to the conjectured value n. The more general problem of random greedy pa...
متن کاملA note on the random greedy triangle-packing algorithm
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on n vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is chosen uniformly at random from the collection of all remaining triangles. This stochastic process terminates once it arrives at a triangle-free graph. In ...
متن کاملRandom greedy triangle-packing beyond the 7/4 barrier
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. Begin with a complete graph on n vertices and proceed to remove the edges of triangles one at a time, where each triangle removed is chosen uniformly at random out of all remaining triangles. This stochastic process terminates once it arrives at a triangle-free graph, and a longstanding ope...
متن کاملNP-Hard Triangle Packing Problems
In computational geometry, packing problems ask whether a set of rigid pieces can be placed inside a target region such that no two pieces overlap. The triangle packing problem is a packing problem that involves triangular pieces, and it is crucial for algorithm design in many areas, including origami design, cutting industries, and warehousing. Previous works in packing algorithms have conject...
متن کاملGreedy Online Bipartite Matching on Random Graphs
We study the average performance of online greedy matching algorithms on G(n, n, p), the random bipartite graph with n vertices on each side and edges occurring independently with probability p = p(n). In the online model, vertices on one side of the graph are given up front while vertices on the other side arrive sequentially; when a vertex arrives its edges are revealed and it must be immedia...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1997
ISSN: 1077-8926
DOI: 10.37236/1296