Cs6515 - Study guides, Class notes & Summaries

Weak Duality Theorem Feasible x <= Feasible y where c^(zT) x <= b^(T) y. Here c^(T) means transpose and same for b^(T). Weak Duality Theorem Corollary 1 If Feasible x = Feasible y, they are optimums c^(T) x^(asterisk) = b^(T) y^(asterisk) . Weak Duality Theorem Corollary 2 If Primal/Dual is unbounded, then Dual/Primal is infeasible Strong Duality Theorem Primal is feasible and bounded IFF <=> Dual is feasible and bounded. Primal has a optimum x^(asterisk) iff dual has optimu...

Basic Properties of Trees - ANSWER-Tree's are undirected, connected and acyclic that connect all nodes. 1. Tree on n vertices has (n-1) edges -> would have a cycle otherwise (more than n-1 edges means cycle) 2. In tree exactly one path between every pair of vertices (otherwise it's not connected) - More than 1 path implies cycle - less than 1 path implies not connected 3. Any connected G(V, E) with |E| = |V| - 1 is a tree Kruskal's Algorithm - ANSWER-1. Sort E by increasing weigt ...

Knapsack without repetition - ANSWER-k(0) = 0 for w = 1 to W: if w_j >w: k(w,j) = k(w, j - 1) else: K(w,j) = max{K(w, j -1),K(w - w_j, j -1) + v_i} knapsack with repetition - ANSWER-knapsack repeat(w_i....w_n, w_i... w_n, B) k(0) = 0 for i = 1 to n if w_i <= b & k(b) <v_i + K(b-w_i) then k(b) = v_i + K(b-w_i) Longest Increasing Subsequence - ANSWER-LIS(a_1.... a_n) for i = 1 to n L(i) = 1 for j = 1 to n -1 if a_j < a_i & L(i) < 1 + L(j) L(i) = 1 + L(j) max = 1 for ...

CS6515 Exam 3 with complete solution

CS6515 Exam 2 | Questions and Correct Answers | Latest Update 2024/2025 | Graded A+ Basic Properties of Trees - Answer -Tree's are undirected, connected and acyclic that connect all nodes. 1. Tree on n vertices has (n-1) edges -> would have a cycle otherwise (more than n-1 edges means cycle) 2. In tree exactly one path between every pair of vertices (otherwise it's not connected) - More than 1 path implies cycle - less than 1 path implies not connected 3. Any connected G(V, E) wi...

CS6515 Exam 3 questions and answers

Cs6515 Exam 3 with complete solution

CS6515 Exam 3 Actual Set Questions & Revised Correct Answers PASSED!! What is a P problem? - ANSWER : P = Polynomial -A problem that can be solved in Polynomial time. -There is a Polynomial time algorithm to solve it. What is a NP problem? - ANSWER : NP = NonDeterministically Polynomial -A problem where the Solution can be VERIFIED in Polynomial-Time What are differences in P and NP? - ANSWER : All P problems are in NP but all NP problems are not in P. P is a subset of NP. -Pr...

CS6515 Exam 2 Questions and answers If graph G has more than |V | − 1 edges, and there is a unique heaviest edge, then this edge cannot be part of a minimum spanning tree - ANSWER-False, because the unique heaviest edge may not be part of a cycle If G has a cycle with a unique heaviest edge e, then e cannot be part of any MST. - ANSWER-True, if the unique heaviest edge is part of a cycle then it will be removed first. Let e be any edge of minimum weight in G. Then e must be part of some...