Branch-and-Bound versus Lift-and-Project Relaxations in Combinatorial Optimization
- Resource Type
- Working Paper
- Authors
- Cornuéjols, Gérard; Dubey, Yatharth
- Source
- Subject
- Mathematics - Optimization and Control
Computer Science - Data Structures and Algorithms
- Language
In this paper, we consider a theoretical framework for comparing branch-and-bound with classical lift-and-project hierarchies. We simplify our analysis of streamlining the definition of branch-and-bound. We introduce "skewed $k$-trees" which give a hierarchy of relaxations that is incomparable to that of Sherali-Adams, and we show that it is much better for some instances. We also give an example where lift-and-project does very well and branch-and-bound does not. Finally, we study the set of branch-and-bound trees of height at most $k$ and effectively "squeeze" their effectiveness between two well-known lift-and-project procedures.