Selfish Bin Covering

In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we mainly concern is how much the lack of coordination harms the social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several other new equilibria. For each equilibrium, the corresponding PoA and PoS are given, and the problems of computing an arbitrary equilibrium, as well as approximating the best one, are also considered.Comment: 16 page

Performance estimations of first fit algorithm for online bin packing with variable bin sizes and LIB constraints

We consider the NP Hard problem of online Bin Packing while requiring that larger (or longer) items be placed below smaller (or shorter) items --- we call such a version the {LIB} version of problems. Bin sizes can be uniform or variable. We provide analytical upper bounds as well as experimental results on the asymptotic approximation ratio for the first fit algorithm

Bin packing and covering with longest items at the bottom: online version

We consider the NP hard problems of online bin packing and online bin covering while requiring that larger (or longer, in the one-dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items. Bin sizes can be uniform or variable. If variable, the bin sizes are drawn from a finite collection. In uniform sized online bin packing, we prove an upper bound of two on the approximation ratio for special cases of the problem and provide computational results for the general case using a variation of the first fit heuristic. In uniform sized online bin covering, we prove a non-approximability result and present a modified first fit heuristic. In online variable-sized bin covering, we show that the approximation ratio guaranteed by our heuristic is a function of bin lengths

Online LIB problems : Heuristics for bin covering and lower bounds for bin packing

We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items - we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for uniform sized bin covering. The Best Fit heuristic for this version of the problem is introduced here. The approximation ratios obtained were well within the theoretical upper bounds. For variable sized bin covering, a more thorough analysis revealed definite trends in the maximum and average approximation ratios. Finally, we prove that for online LIB bin packing with uniform size bins, no heuristic can guarantee an approximation ratio better than 1.76 under the online model considered.C

Optimal on-line algorithms for variable-sized bin covering

We deal with the variable-sized bin covering problem: Given a list L of items in (0,1] and a finite collection of feasible bin sizes, the goal is to select a set of bins with sizes in and to cover them with the items in L such that the total size of the covered bins is maximized. In the on-line version of this problem, the items must be assigned to bins one by one without previewing future items. This note presents a complete solution to the on-line problem: For every collection of bin sizes, we give an on-line approximation algorithm with a worst-case ratio , and we prove that no on-line algorithm can perform better in the worst case. The value mainly depends on the largest gap between consecutive bin sizes