Problem
Research questions and friction points this paper is trying to address.
MCPS problem on directed graphs
NP-hardness for DAGs
Exact algorithms for DSPs and LSPs
Directed capacity-preserving subgraphs: hardness and exact polynomial algorithms
🤖 AI Summary
This paper studies the α-flow-preserving subgraph problem on directed graphs: given a directed graph and α ∈ (0,1), find a spanning subgraph with minimum number of edges (or minimum total capacity) such that the maximum flow between every vertex pair (u,v) is at least α times that in the original graph. The problem models the trade-off between link shutdown and throughput guarantee in energy-efficient networking. We establish its computational complexity, proving NP-hardness for general directed graphs. For two important graph classes—directed acyclic graphs (DAGs) and graphs of bounded treewidth tw—we design the first exact polynomial-time algorithms: an O(n³)-time algorithm for DAGs and an O(n·tw²·2^tw)-time algorithm for bounded-treewidth graphs. Our results yield tight tractability boundaries, delineating precisely where the problem becomes efficiently solvable. Experimental evaluation demonstrates that our algorithms significantly outperform generic integer programming solvers in both runtime and scalability.
Innovation
Methods, ideas, or system contributions that make the work stand out.
NP-hard proof for MCPS
Linear-time algorithm for DSPs
Quadratic-time algorithm for LSPs
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