منابع مشابه
2 Packing and Covering
The basic problems in the classical theory of packings and coverings, the development of which was strongly influenced by the geometry of numbers and by crystallography, are the determination of the densest packing and the thinnest covering with congruent copies of a given body K. Roughly speaking, the density of an arrangement is the ratio between the total volume of the members of the arrange...
متن کاملOnline Mixed Packing and Covering
In many problems, the inputs to the problem arrive over time. As each input is received, it must be dealt with irrevocably. Such problems are online problems. An increasingly common method of solving online problems is to solve the corresponding linear program, obtained either directly for the problem or by relaxing the integrality constraints. If required, the fractional solution obtained is t...
متن کاملPacking and covering induced subdivisions
A graph class $\mathcal{F}$ has the induced Erd\H{o}s-P\'osa property if there exists a function $f$ such that for every graph $G$ and every positive integer $k$, $G$ contains either $k$ pairwise vertex-disjoint induced subgraphs that belong to $\mathcal{F}$, or a vertex set of size at most $f(k)$ hitting all induced copies of graphs in $\mathcal{F}$. Kim and Kwon (SODA'18) showed that for a cy...
متن کاملPacking and Covering Dense Graphs
Let d be a positive integer. A graph G is called d-divisible if d divides the degree of each vertex of G. G is called nowhere d-divisible if no degree of a vertex of G is divisible by d. For a graph H, gcd(H) denotes the greatest common divisor of the degrees of the vertices of H. The H-packing number of G is the maximum number of pairwise edge disjoint copies of H in G. The H-covering number o...
متن کاملCombinatorial Optimization: Packing and Covering
1 Preface The integer programming models known as set packing and set covering have a wide range of applications, such as pattern recognition, plant location and airline crew scheduling. Sometimes, due to the special structure of the constraint matrix, the natural linear programming relaxation yields an optimal solution that is integer, thus solving the problem. Sometimes, both the linear progr...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1988
ISSN: 0898-1221
DOI: 10.1016/0898-1221(88)90211-8