DeepAI AI Chat
Log In Sign Up

Solutions for Subset Sum Problems with Special Digraph Constraints

by   Frank Gurski, et al.

The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with weak digraph constraint (SSGW). In both problems there is given a digraph with sizes assigned to the vertices. Within SSG we want to find a subset of vertices whose total size does not exceed a given capacity and which contains a vertex if at least one of its predecessors is part of the solution. Within SSGW we want to find a subset of vertices whose total size does not exceed a given capacity and which contains a vertex if all its predecessors are part of the solution. SSG and SSGW have been introduced recently by Gourves et al. who studied their complexity for directed acyclic graphs and oriented trees. We show that both problems are NP-hard even on oriented co-graphs and minimal series-parallel digraphs. Further, we provide pseudo-polynomial solutions for SSG and SSGW with digraph constraints given by directed co-graphs and series-parallel digraphs.


page 1

page 2

page 3

page 4


Finding a Maximum-Weight Convex Set in a Chordal Graph

We consider a natural combinatorial optimization problem on chordal grap...

On Maximum Common Subgraph Problems in Series-Parallel Graphs

The complexity of the maximum common connected subgraph problem in parti...

Improved Approximation Schemes for (Un-)Bounded Subset-Sum and Partition

We consider the SUBSET SUM problem and its important variants in this pa...

Finding (s,d)-Hypernetworks in F-Hypergraphs is NP-Hard

We consider the problem of computing an (s,d)-hypernetwork in an acyclic...

Efficient computation of oriented vertex and arc colorings of special digraphs

In this paper we study the oriented vertex and arc coloring problem on e...

A Simple and Elegant Mathematical Formulation for the Acyclic DAG Partitioning Problem

This work addresses the NP-Hard problem of acyclic directed acyclic grap...

A Probabilistic Approach to The Perfect Sum Problem

The subset sum problem is known to be an NP-hard problem in the field of...