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the alldiff-except-0x constraint requires the variables x1xn with nonzero values to take different valuesindicate how
prove theorem 1 as a corollary of theorem 2hint add a source and sink and view the matching problem as a flow
prove theorem 1 as a corollary of theorem 2hint look at the conditions for whether the current flow of zero on edge e
formulate a flow model that can be used to achieve domain consistency for the constraint nvalues xl uhint some
let g be a directed acyclic graph on n vertices in which each edge i j has length cijstate a dynamic programming
consider the 3-machine disjunctive scheduling problem in whiche1 e2 e3 2 1 0 l1 l2 l3 6 5 8 p 3 2 2use the
apply the polynomial-time edge-finding algorithm to the problem of exerciseexercise consider the 3-machine disjunctive
apply the polynomial-time not-first algorithm to the example of exerciseexercise consider the 3-machine disjunctive
indicate how sensitivity analysis based on a branching tree can be extended to general integer programming assume that
complete the solution of 390 by benders decomposition based on the branching dualequationmin
suppose one is given initial domains y isin 1 2 3 x isin -1 cup 1 3 and z isin -2 -1 cup 1 2reduce domains to achieve
let the system gx ge 0 of inequalities imply fx ge v for x isin s when there is a u ge 0 such that ugx le fx - v -
show that lagrangean duality reduces to linear programming duality when gx ax-b and s x x ge 0it suffices to show
it is impossible to put three pigeons in two pigeon holes with at most one pigeon per holeprove this by the resolution
prove theorem 320hints prove the theorem first for horn clauses then note that a unit resolution proof before renaming
a 2-satisfiability 2sat problem is a cnf problem with at most two literals in each clauseshow that 3-resolution which
formulate the problem of checking whether a clause set is renamable horn as a 2sat problemfor each of the n variables
suppose that constraint set s contains only boolean variables and suppose that every clause that is implied by a
two families are meeting for partyone family consists of jane robert and suzie and the other consists of juan maria and
let a multivalent clause have the form j xj isin sj where each xj has a finite domain dxj and each sj sub dxjgeneralize
show by counterexamples that neither absorbsion nor reduction is a necessary condition for implication between 0-1
consider the inequalities x1 x2 ge 1 x1 - x2 ge 0 with each xj isin 0 alphafor what values of alpha ge 0 does bounds
suppose that the problem in exercise 10 is the continuous relaxation of an integer programming problem ie the same
what is the minimum makes pan on machine a in the exercisewhat jobs play a role in deriving the minimum trace the
a number of projects must be carried out in a shop and each project j must start and finish within a time window rj