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Extra info for A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

Sample text

Conjunct A predicate that’s ANDed with zero or more others. conjunction 1. (Dyadic case) If p and q are predicates, their conjunction (p) AND (q) is a predicate also. Let (ip) AND (iq) be an invocation of that predicate (where ip and iq are invocations of p and q, respectively). Then that invocation (ip) AND (iq) evaluates to TRUE if and only if ip and iq both evaluate to TRUE. Note: The parentheses enclosing p and q in the conjunction might not be needed in practice. 2. (N-adic case) Let p1, p2, .

Example: Let s1 be the set of nonnegative integers {0,1,2, . } and let two such integers be equivalent if and only if they leave the same remainder on division by five. Then we can define s2 to be the set {0,1,2,3,4}. As for an “interesting” theorem that applies in this example, let x1, y1, and z1 be any three elements of s1, and let their canonical forms in s2 be x2, y2, and z2, respectively; then the product y1 * z1 is equivalent to x1 if and only if the product y2 * z2 is equivalent to x2. cardinality The number of elements in a bag or (especially) set; of a relation, the number of tuples in the body of that relation.

Bag membership (Of an element) The property of appearing in some given bag; the operation of testing for that property. , bag membership is usually denoted by the symbol “∈”; thus, the Boolean expression x ∈ b returns TRUE if and only if element x does in fact appear at least once in bag b. bag operator See bag. base relation The value of a given base relvar at a given time. Contrast derived relation. Examples: The relations that are the values of relvars S, P, and SP at any given time. base relvar A relvar not defined in terms of others; that is, an independent relvar.

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A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem by Sbihi A.


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