Linked Questions

0
votes
1answer
974 views

Is Weighted Vertex Cover NP-Complete? [duplicate]

I'm doing practice problems for an upcoming exam and I'm unsure if the following problem is NP-complete. If it is can you please give me a hint as to what problem I should reduce to it. I believe it's ...
1
vote
0answers
29 views

When proving a problem is NP-C, how do I select another NP-C problem for the transformation? [duplicate]

I'm taking an algorithms course in which we are discussing proofs that problems are NP-Complete. Our proofs usually take the form: Given a problem $\Pi$, 1. Prove that $\Pi$ is NP. 2. Select an NP-...
0
votes
0answers
27 views

HITTING SET Problem [duplicate]

HITTING SET INSTANCE: collection C of subsets of a set S, positive integer K. QUESTION: Does C contain a hitting set for C of size K or less, that is, a subset S' of S with |S'| <= K and such ...
40
votes
4answers
14k views

What are common techniques for reducing problems to each other?

In computability and complexity theory (and maybe other fields), reductions are ubiquitous. There are many kinds, but the principle remains the same: show that one problem $L_1$ is at least as hard as ...
2
votes
3answers
637 views

Prove that finding largest subset of undirected graph that is almost independent is NP-hard

A subset $S$ of vertices in an undirected graph $G$ is called almost independent if at most 100 edges in $G$ have both endpoints in $S$. Prove that finding the size of the largest almost-independent ...
0
votes
1answer
441 views

NP Completeness of 3-SAT problem [closed]

I have started reading on algorithmic complexity for my thesis work. Already have studied on Polynomial time reducibility, NP-Complete, NP-Hard. Now trying to prove NP completeness of some of the ...
3
votes
3answers
118 views

Has anyone seen a NP graph problem like this before?

I have a following graph-based problem: Input: positive integers K and L, undirected graph G I have to choose K vertices from this graph In the path between each pair of chosen K vertices there ...
2
votes
2answers
521 views

Negative simple path NP-Complete

Given a graph $G=(V,E)$, and positive and negative edge weights, negative path problem asks if there is a simple path with negative total weight from $s$ to $t$ where $s,t \in V$ My approach was to ...
2
votes
2answers
126 views

How to prove NP-hardness from scratch?

I am working on a problem of whose complexity is unknown. By the nature of the problem, I cannot use long edges as I please, so 3SAT and variants are almost impossible to use. Finally, I have decided ...
6
votes
2answers
77 views

Sequence to explore the complexity of the NP problem

Let $X$ be some problem known to be in $NP$. What is the natural next step in exploring the complexity of the problem? Is it trying to prove whether it is in $P$ or try to prove it is $NP$-Hard? ...
0
votes
1answer
539 views

Proof NP-Complete for Single machine Job Scheduling Problem specific version

Problem: given a set of n tasks with execution time Ti, due date Di, and a profit Vi (given only if is enden before due date), is there a task schedule that returns a total profit greater or equal ...
1
vote
1answer
310 views

DFA accepts common strings, reduction to NPcomplete

$B=\{\left<M_1,M_2,...,M_k\right>\text{ : Each $M_i$ is a DFA and all of the $M_i$ accept some common string.} \}$ I'm trying to show that B is NP-complete. I know I have to reduce it to ...
2
votes
1answer
415 views

4-partition elements summation NP completeness

How can we prove that the following problem $A$ is NP complete? Given a set of integers $S={a_1, ..., a_n}$ and a number $D$, is it possible to find disjoint sets $S_1, S_2, S_3, S_4$ such that $S_1 \...
2
votes
2answers
250 views

Check if K-Sum Variation is NP-Complete

Problem Given a range of integers $\{a,a+1,...,b-1,b\}$, find a subset of size $k$ such that the sum is equal to $s$. Question This problem came from evaluating some scheduling algorithms that I am ...
-2
votes
2answers
316 views

Find a simple path through a graph, vising as many vertices in Z as possible

Goal: Find a simple path in G, that visits the maximum number of vertices in Z and prove it is NP-complete. G = (V , E) Z is a subset of V How would I go about doing this?

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