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question consider the weighted min-vc where every vertex has been assigned a positive integer weight and the task is to
question the maximum matching problem is to find a matching of maximum cardinality in a given graph g express any
question what do min-vc and min-sc have in common can one consider one of these problems as a special case of the
question let k be a positive integer consider min-sck as the following restricted version of min-sc the instances of
question modify primegen l k in such a way that it must run until it outputs a number n this means that one forbids the
question let p be a prime and let k le log2p be a positive integer design an efficient las vegas algorithm that
question modify the algorithm nquad in such a way that it always halts with a quadratic nonresidue ie the answer never
question modify the algorithm contraction in the following way instead of choosing an edge at random choose two
question let u v sube 0 1n and let u isin o n3 and v isin o n2 how many independent runs of pdisj are necessary ie
question the disjointness problem for an instance u v can be solved by a deterministic protocol by sending the
question apply this success amplification method to the protocols pset and pdisj and estimate the error probability as
question compare the amplification method of executing independent runs with the method of increasing the size of the
question consider a network of l computers r1 r2 rl in which each computer is directly connected via a communication
question show that a graph is bipartite if and only if it does not have a circuit with an odd number of edgesexercise a
question extend the algorithm schoning for 4sat observe that the lower bound on the probability of moving toward
question let g be a connected graph and let c be any circuit in g that does not contain every vertex of c let g be the
question a prove that if a walk in a graph contains a repeated edge then the walk contains a repeated vertexb explain
question a traveler in europe wants to visit each of the cities shown on the map exactly once starting and ending in
question for what values of m and n does the complete bipartite graph on m n vertices havea an euler circuitb a
question determine which of the graphs have euler circuits if the graph does not have an euler circuit explain why not
question the solution for example shows a graph for which every vertex has even degree but which does not have an euler
question each of a-c describes a graph in each case answer yes no or not necessarily to this question does the graph
question in find hamiltonian circuits for those graphs that have them explain why the other graphs do
question determine whether there is a primary key for the relation in exampleexample let r be the relation on z times z
question discuss the use of the critical path method cpm to find the shortest time for the completion of a project how