
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Input: a group G acting on f2;
an invariant partition n = {B 1 IB2 I... IBt} of f~;
the corresponding blocks homomorphism t~;
a base B = [i 1,i2 ..... ~] of imgp;
a strong generating set T of a subgroup H of im~ relative to the base B;
a base and strong generating set of ker(p;
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- 15arrow_forwardBacktrack Search Algorithm Using Known Subgroupa group G with the base B=[51, 132,..... k] and a strong generating set S as the input; a subgroup L of G whose members meet the decidable condition P;a powerful generating set with respect to B for the subgroup K = H (P);arrow_forwardAlgorithm to Determining an orbit and Schreier vectorInput : a set S = {s 1, s2 ..... Sm} of generators of a group G acting on f2; a point 5;Output : the orbit ~G; a Schreier vector v and backward pointers w of the orbit 8 G relative to the set S of generators;arrow_forward
- Exercise c. Strict matchingConsider the following generalization of the maximum matching problem, which we callStrict-Matching. Recall that a matching in an undirected graph G = (V, E) is a setof edges such that no distinct pair of edges {a, b} and {c, d} have endpoints that areequal: {a, b} ∩ {c, d} = ∅. Say that a strict matching is matching with the propertythat no pair of distinct edges have endpoints that are connected by an edge: {a, c} ̸∈ E,{a, d} ̸∈ E, {b, c} ̸∈ E, and {b, d} ̸∈ E. (Since a strict matching is also a matching, wealso require {a, b} ∩ {c, d} = ∅.) The problem Strict-Matching is then given a graphG and an integer k, does G contain a strict matching with at least k edges.Prove that Strict-Matching is NP-complete.arrow_forwardOn S = f2; 4; 6; 10; 12; 20; 30; 60g we work with the divisibility relation R:xRy , x divides y:(i) Draw the Hasse diagram of R.(ii) Find all R-minimal elements.(iii) Find all R-maximal elements.(iv) Find all non-empty subsets U S, so that 6 is an R-lowerbound of U.(v) Let A = f6; 10; 12g. If A admits an R-supremum, nd it. If A admits an R-in mum, nd it.(vi) Is R a lattice?arrow_forwardAlgorithm for Backtrack Search Restricting Choice of Base ImagesInput : a group G with a base B=[[51, [52 ..... [sk] and a strong generating set S;a decidable property P whose elements form a subgroup;Output : a strong generating set relative to B for the subgroup K = H (P) ;procedure search( G : group; P: property; s : 1..k+l; var K : group );(* Search G (s) for the subgroup K of elements satisfying P. *)arrow_forward
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