Question: Prove that the following 2-Sets decision problem is NP-complete. The input is a set of numbers {w1, . . . , wn} and a bound

Prove that the following 2-Sets decision problem is NP-complete. The input is a set of numbers {w1, . . . , wn} and a bound M. The question is: can {1, 2, . . . , n} be divided into two sets A, B (where A B = {1, 2, . . . , n} and A B = ) such that P P iA wi M and iB wi M. Hint: As a warmup consider the version where you are given two bounds MA and MB and the requirement is that P iA wi MA and P iB wi MB

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Give Correct ANSWERS Human-Computer Interaction (a) If you had been one of the original inventors of the WIMP interface, and engineers on the technical team had been sceptical about the advantages...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

1456HHSC attend all (a) In the quantum teleportation protocol, Alice and Bob are every in possession of one qubit of a couple in the joint country00i + statei. Explain how the protocol works. In...

You have been provided with the description of a programming language, J, intended for scripting applications. Its syntax is similar to a cut-down version of Java in that it consists of function...

Describe, and estimate the costs of, procedures to (a) insert a new item into an existing heap; (b) delete the topmost item from a non-empty heap; (c) starting from an array holding N items in...

What is a branch delay slot and why does it arise? [7 marks] How can branch delays be avoided? If a processor exhibited one branch delay slot how would you reorder (and possibly modify) the...

"There is a growing interdependence between a firm's ability to use information technology and its ability to implement corporate strategies and achieve corporate goals." "To fully understand...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

hen we contrive an assumption that the existence of primitive recursive functions pair N 2 N, fst N N and snd N N satisfying for all x, y N fst(pair (x, y)) = x snd(pair (x, y)) = y prove by...

Accounts payableCustomer refunds payableDelivery expenseFreight inPurchasesPurchases discounts purchases returns and allowancesSalesSupplies expenseLabelsApril 30, 2018For the Year Ended April 30,...

On 1 January 2011 Khumalo Ltd acquired a patent for R250, 000. On 31 December 2011 management assessed the patents useful life at 15 years from the date of acquisition. Management assessed that the...

Which of the following are the two operational components of central bank independence? Multiple choice question. Freedom from media criticism and no considerations required in exchange for budgetary...

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.