87 research outputs found
0-1 Integer Linear Programming with a Linear Number of Constraints
We give an exact algorithm for the 0-1 Integer Linear Programming problem
with a linear number of constraints that improves over exhaustive search by an
exponential factor. Specifically, our algorithm runs in time
where n is the number of variables and cn is the
number of constraints. The key idea for the algorithm is a reduction to the
Vector Domination problem and a new algorithm for that subproblem
Fixed parameter tractability of crossing minimization of almost-trees
We investigate exact crossing minimization for graphs that differ from trees
by a small number of additional edges, for several variants of the crossing
minimization problem. In particular, we provide fixed parameter tractable
algorithms for the 1-page book crossing number, the 2-page book crossing
number, and the minimum number of crossed edges in 1-page and 2-page book
drawings.Comment: Graph Drawing 201
On Exact Algorithms for Permutation CSP
In the Permutation Constraint Satisfaction Problem (Permutation CSP) we are
given a set of variables and a set of constraints C, in which constraints
are tuples of elements of V. The goal is to find a total ordering of the
variables, , which satisfies as many
constraints as possible. A constraint is satisfied by an
ordering when . An instance has arity
if all the constraints involve at most elements.
This problem expresses a variety of permutation problems including {\sc
Feedback Arc Set} and {\sc Betweenness} problems. A naive algorithm, listing
all the permutations, requires time. Interestingly, {\sc
Permutation CSP} for arity 2 or 3 can be solved by Held-Karp type algorithms in
time , but no algorithm is known for arity at least 4 with running
time significantly better than . In this paper we resolve the
gap by showing that {\sc Arity 4 Permutation CSP} cannot be solved in time
unless ETH fails
Lightsolver challenges a leading deep learning solver for Max-2-SAT problems
Maximum 2-satisfiability (MAX-2-SAT) is a type of combinatorial decision
problem that is known to be NP-hard. In this paper, we compare LightSolver's
quantum-inspired algorithm to a leading deep-learning solver for the MAX-2-SAT
problem. Experiments on benchmark data sets show that LightSolver achieves
significantly smaller time-to-optimal-solution compared to a state-of-the-art
deep-learning algorithm, where the gain in performance tends to increase with
the problem size
- …