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requires calculus a let n be a positive integera show that the relation r on the set of all polynomials with
let r be the relation on the set of all sets of real numbers such that srt if and only if s and t have the same
define three equivalence relations on the set of buildings on a college campus determine the equivalence classes for
define three equivalence relations on the set of classes offered at your school determine the equivalence classes for
show that the relation of logical equivalence on the set of all compound propositions is an equivalence relation what
let r be the relation on the set of all urls or web addresses such that xry if and only if the web page at x is the
devise an algorithm based on the concept of interior vertices that finds the length of the longest path between two
show that the transitive closure of the symmetric closure of the reflexive closure of a relation r is the smallest
a let s be the set of subroutines of a computer program define the relation r by pr q if subroutine p calls subroutine
given the matrix representing a relation on a finite set find the matrix representing the smallest equivalence relation
given the matrix representing a relation on a finite set find the matrix representing the transitive closure of this
given any positive integer na find a connected graph with n edges such that removal of just one edge disconnects the
a traveler in europe wants to visit each of the cities shown on the map exactly once starting and ending in brussels
a prove that if a walk in a graph contains a repeated edge then the walk contains a repeated vertexb explain how it
extend the algorithm schoning for 4sat observe that the lower bound on the probability of moving toward alphalowast in
modify the algorithm contraction in the following way instead of choosing an edge at random choose two vertices x and y
modify primegen l k in such a way that it must run until it outputs a number n this means that one forbids the output i
the maximum matching problem is to find a matching of maximum cardinality in a given graph g express any instance of
find an infinite set of input instances of max-sat for which the expected solutions computed by rsam are better than
implement the algorithm comb and test it for real max-sat instances try to estimate the average approximation ratio
let k be a positive integer consider min-sck as the following restricted version of min-sc the instances of min-sck are
what do min-vc and min-sc have in common can one consider one of these problems as a special case of the
consider the weighted min-vc where every vertex has been assigned a positive integer weight and the task is to minimize
in an old puzzle attributed to alcuin ofyork 735-804 a farmer needs to carry a wolf a goat and a cabbage across a river