The multiple weighted hitting set problem is to find a subset of nodes in a hypergraph that hits every hyperedge in at least m nodes. We extend the problem to a notion of hypergraphs with so-called hypernodes and show that, for m = 2, it remains fixed-parameter tractable (FPT), parameterized by the number of hyperedges. This is accomplished by a nontrivial extension of the dynamic programming a...

In the double TSP with multiple stacks, a vehicle with several stacks performs a Hamiltonian circuit to pick up some items and stores them in its stacks. It then delivers every item by performing another Hamiltonian circuit while satisfying the last-in-first-out policy of its stacks. The consistency requirement ensuring that the pickup and delivery circuits can be performed by the vehicle is th...

We use a new approximation measure, the differential approximation ratio, to derive polynomial-time approximation algorithms for minimum set covering (for both weighted and unweighted cases), minimum graph coloring and bin-packing. We also propose differentialapproximation-ratio preserving reductions linking minimum coloring, minimum vertex covering by cliques, minimum edge covering by cliques ...

Abstract Consider the following variant of the set cover problem. We are given a universe U = {1, ..., n} and a collection of subsets C = {S1, ..., Sm} where Si ⊆ U . For every element u ∈ U we need to find a set φ (u) ∈ C such that u ∈ φ (u). Once we construct and fix the mapping φ : U 7→ C a subset X ⊆ U of the universe is revealed, and we need to cover all elements from X with exactly φ(X) :...

We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis dimension (VC-dimension) of the input is small. VC-dimension is a natural measure of complexity of set systems. Several tractable instances of Hitting Set with a ge...

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in the absence of herbicides, cover crops play an important role for weed management in organic than in conventional farming. therefore, in order to evaluate the effects of cover crop management and plant density of buckwheat (fagopyrum esculentum) as cover crop on weed suppression, a field experiment was conducted at the research farm of university of zanjan, during the growing season of 2011....

Let G be a simple (i.e., no loops and no multiple edges) graph. We investigate the question of how to modify G combinatorially to obtain a sequentially CohenMacaulay graph. We focus on modifications given by adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex in G. We give various sufficient conditions and...

Let G = (V,E) be a graph and R ⊆ E. A matching M in G is called R-feasible if the subgraph induced by the M -saturated vertices does not have an edge of R. We show that the general problem of finding a maximum size Rfeasible matching in G is NP-hard and identify several natural applications of this new concept. In particular, we use R-feasible matchings to give a necessary and sufficient condit...