972 research outputs found
Combinatorial persistency criteria for multicut and max-cut
In combinatorial optimization, partial variable assignments are called
persistent if they agree with some optimal solution. We propose persistency
criteria for the multicut and max-cut problem as well as fast combinatorial
routines to verify them. The criteria that we derive are based on mappings that
improve feasible multicuts, respectively cuts. Our elementary criteria can be
checked enumeratively. The more advanced ones rely on fast algorithms for upper
and lower bounds for the respective cut problems and max-flow techniques for
auxiliary min-cut problems. Our methods can be used as a preprocessing
technique for reducing problem sizes or for computing partial optimality
guarantees for solutions output by heuristic solvers. We show the efficacy of
our methods on instances of both problems from computer vision, biomedical
image analysis and statistical physics
A Parallelizable Acceleration Framework for Packing Linear Programs
This paper presents an acceleration framework for packing linear programming
problems where the amount of data available is limited, i.e., where the number
of constraints m is small compared to the variable dimension n. The framework
can be used as a black box to speed up linear programming solvers dramatically,
by two orders of magnitude in our experiments. We present worst-case guarantees
on the quality of the solution and the speedup provided by the algorithm,
showing that the framework provides an approximately optimal solution while
running the original solver on a much smaller problem. The framework can be
used to accelerate exact solvers, approximate solvers, and parallel/distributed
solvers. Further, it can be used for both linear programs and integer linear
programs
The matching relaxation for a class of generalized set partitioning problems
This paper introduces a discrete relaxation for the class of combinatorial
optimization problems which can be described by a set partitioning formulation
under packing constraints. We present two combinatorial relaxations based on
computing maximum weighted matchings in suitable graphs. Besides providing dual
bounds, the relaxations are also used on a variable reduction technique and a
matheuristic. We show how that general method can be tailored to sample
applications, and also perform a successful computational evaluation with
benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented
at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial
Optimization), with proceedings on Electronic Notes in Discrete Mathematic
- …