Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

Questions tagged [partition-problem]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
8
votes
2answers
1k views

Faster pseudo-polynomial time algorithms for PARTITION

I want to partition N given numbers (may or may not be equal) into 2 subsets such that the 2 subsets have sum as close as possible and also the cardinality of the sets are equal (if n is even) or ...
13
votes
1answer
492 views

Partition into interval graphs

Suppose there is a graph $G=(V,E)$. I want to test if $V$ can be partitioned into two disjoint sets $V_1$ and $V_2$ such that the subgraphs induced by $V_1$ and $V_2$ are unit interval graphs. I know ...
13
votes
1answer
739 views

Intermediate $\mathsf{NP}$-complete problems?

Partition problem is weakly NP-complete since it has polynomial (pseudo-polynomial) time algorithm if input integers are bounded by some polynomial. However, 3-Partition is strongly NP-complete ...
7
votes
2answers
1k views

Partition a graph into 2 connected subgraphs

I'm stumped on a sub problem that I'm working on for my thesis. I need to be able to partition a graph into 2 connected subgraphs of almost equal size. So if there are $m$ vertices in $G$, subgraphs $...
4
votes
1answer
400 views

Proof that the graph optimization problem is NP-hard

I'm trying to prove that the following optimization problem is NP-hard: Given a graph $G=(V,E)$, non-negative vertex weight functions $w(v)$ and $s(v)$, and a non-negative edge weight function $t(u,v)...
2
votes
2answers
557 views

Strongly NP-complete variants of subset sum or partition problem

Some problems have variants that appear to be harder. For instance, Graph Automorphism (GA) problem has quasi-polynomial time algorithm ( by Babai's GI result). However, the fixed-point free GA ...