We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant , there exists a polynomial-time approximation algorithmwith an asymptotic worst-case performance ratio of no more than 1 + .

In the paper, we investigate the pair frequency of low-level heuristics for the bin packing problem and propose a Frequency Distribution based Hyper-Heuristic (FDHH). FDHH generates the heuristic sequences based on a pair of low-level heuristics rather than an individual low-level heuristic. An existing Simulated Annealing Hyper-Heuristic (SAHH) is employed to form the pair frequencies and is e...

We show that the analogue of Hamilton’s Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston’s circle packing on surfaces. As a consequence, a new proof of Thurston’s existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings.

We study the following problem, introduced by Chung et al. in 2006. We are given, online or offline, a set of coloured items of different sizes, and wish to pack them into bins of equal size so that we use few bins in total (at most α times optimal), and that the items of each colour span few bins (at most β times optimal). We call such allocations (α, β)-approximate. As usual in bin packing pr...

In this paper we present algorithms with optimal average-case and close-to-best known worst-case performance for the classic online bin packing problem. It has long been observed that known bin packing algorithms with optimal average-case performance are not optimal in the worst-case. In particular First Fit and Best Fit have optimal asymptotic average-case ratio of 1 but a worstcase competitiv...

Best-t is the best known algorithm for on-line bin-packing, in the sense that no algorithm is known to behave better both in the worst case (when Best-t has performance ratio 1.7) and in the average uniform case, with items drawn uniformly in the interval 0; 1] (then Best-t has expected wasted space O(n 1=2 (log n) 3=4)). In practical applications, Best-t appears to perform within a few percent...

The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the "HARMONIC" algorithms Hk introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (1985), pp. 562-572 ]. The algorithms in this paper guarantee the worst case performance of Hk, whereas they only use O(log log k) instead ofk active bins. For k >_6, the algorithms in this paper outpe...

Preparing equipment for transport is one of the core aspects that should be considered by transporter. Storing digital evidence requires extensive care in order to prevent damage of electronic evidence. Digital evidence is sensitive to magnetic fields thus it should be stored in the right manner. When documenting evidence, responder should be cautious of things such as temperature, static elect...

The effect of vacuum packing on the shelf-life of sausages produced from Capoeta umbla were investigated during storage periods. For this purpose, microbial, chemical and sensory changes were analyzed throughout the storage time. The microbial flora of the sausages comprised mainly mesophilic bacteria, psychrotrophic bacteria, lactic acid bacteria, yeast and molds. Escherichia coli, Staphylcocc...

The effect of vacuum packing on the shelf-life of sausages produced from Capoeta umbla were investigated during storage periods. For this purpose, microbial, chemical and sensory changes were analyzed throughout the storage time. The microbial flora of the sausages comprised mainly mesophilic bacteria, psychrotrophic bacteria, lactic acid bacteria, yeast and molds. Escherichia coli, Staphylcocc...