### Table 1 summarizes the two key, defining dimensions of the four multicontainer problems we study in this paper. One key dimension is whether the problem involves packing a set of items into containers so that the container capacity is not exceeded (packing), or whether the problem requires satisfying the quota associated with a container (covering). Another key dimension is whether all of the items must be assigned to bins, or whether only a subset of items are selected to be assigned to bins. A third dimension (not shown in the table) is the set of item attributes (e.g., weight, profit/cost). Bin packing and bin covering are single-attribute problems (items have weight only), while the multiple knapsack and min-cost covering problems are two-attribute problems (items have weight and profit/cost). We focus on the bin packing, bin covering, MKP, and MCCP problems because we believe that these are in some sense the most basic multicontainer problems. Many combinatorial optimization problems can be viewed as extensions of these problems with additional constraints. For example, the generalized assignment problem can be considered a generalization of a MKP with a more complex profit function.

"... In PAGE 6: ... Table1 : Characterizing multicontainer problems.... ..."

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### Table 1 summarizes the two key, defining dimensions of the four multicontainer problems we study in this paper. One key dimension is whether the problem involves packing a set of items into containers so that the container capacity is not exceeded (packing), or whether the problem requires satisfying the quota associated with a container (covering). Another key dimension is whether all of the items must be assigned to bins, or whether only a subset of items are selected to be assigned to bins. A third dimension (not shown in the table) is the set of item attributes (e.g., weight, profit/cost). Bin packing and bin covering are single-attribute problems (items have weight only), while the multiple knapsack and min-cost covering problems are two-attribute problems (items have weight and profit/cost). We focus on the bin packing, bin covering, MKP, and MCCP problems because we believe that these are in some sense the most basic multicontainer problems. Many combinatorial optimization problems can be viewed as extensions of these problems with additional constraints. For example, the generalized assignment problem can be considered a generalization of a MKP with a more complex profit function.

"... In PAGE 6: ... Table1 : Characterizing multicontainer problems.... ..."

Cited by 1

### Table 1 summarizes the two key, defining dimensions of the four multicontainer problems we study in this paper. One key dimension is whether the problem involves packing a set of items into containers so that the container capacity is not exceeded (packing), or whether the problem requires satisfying the quota associated with a container (covering). Another key dimension is whether all of the items must be assigned to bins, or whether only a subset of items are selected to be assigned to bins. A third dimension (not shown in the table) is the set of item attributes (e.g., weight, profit/cost). Bin packing and bin covering are single-attribute problems (items have weight only), while the multiple knapsack and min-cost covering problems are two-attribute problems (items have weight and profit/cost). We focus on the bin packing, bin covering, MKP, and MCCP problems because we believe that these are in some sense the most basic multicontainer problems. Many combinatorial optimization problems can be viewed as extensions of these problems with additional constraints. For example, the generalized assignment problem can be considered a generalization of a MKP with a more complex profit function.

"... In PAGE 6: ... Table1 : Characterizing multicontainer problems.... ..."

Cited by 1

### Table 3: Advantages and disadvantages of different combinatorial functions Combinatorial

"... In PAGE 21: ... The entire list of combiners used is however much larger. Table3 compares the advantages and disadvantages of each of the functions described above. [21] claims that all ensemble combination methods can be derived out of the basic product and sum combinatorial methods.... ..."

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### Table 1: Combinatorial Bid Example

"... In PAGE 2: ... These multidimensional auctions have performed well in the lab, but also in a number of real-world implementations (see [Cra+04] for combinatorial auctions). Table1 illustrates an example with a combinatorial reverse auction for computer hard drives with 4 suppliers. Each supplier provides a bundled all-or-nothing bid.... ..."

### Table 6: Combinatorial Circuits Testing

1994

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### Table 1: Example Combinatorial Auction

2005

"... In PAGE 2: ... This approach does not make allowances for risk-averse bid-takers who may view a small possibility of very low revenue as unacceptable. Consider the example in Table1 , and the optimal expected rev- enue in the situation where a single bid may be withdrawn. There are three submitted bids for items A and B, the third being a com- bination bid for the pair of items at a value of 190.... In PAGE 4: ... When all variables are set to 0 (see Figure 1(a) branch 3), this is not a solution because the minimum revenue of 190 has not been met, so we try assigning bid3 to 1 (branch 4). This is a valid solu- tion but this variable is brittle because there is a 10% chance that this bid may be withdrawn (see Table1 ). Therefore we need to de- termine if a repair can be formed should it break.... In PAGE 5: ... EXAMPLE 2. Consider the example given in Table1 once more, where the bids also comprise a mutual bid bond of 5% of the bid amount. If a bid is withdrawn, the bidder forfeits this amount and the bid-taker compensates winning bidders whose items are with- drawn when a break occurs elsewhere in the solution.... ..."

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