Related papers: A Learning based Branch and Bound for Maximum Comm…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
Previous work has shown that the problem of learning the optimal structure of a Bayesian network can be formulated as a shortest path finding problem in a graph and solved using A* search. In this paper, we improve the scalability of this…
We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…
We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced…
Several important tasks in medical image analysis can be stated in the form of an optimization problem whose feasible solutions are connected subgraphs. Examples include the reconstruction of neural or vascular structures under…
In this paper, a branch and bound algorithm that incorporates the decision maker's preference information is proposed for multiobjective optimization. In the proposed algorithm, a new discarding test is designed to check whether a box…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general…
This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in…
Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the…
There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized…
Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the…
We apply a branch-and-bound (B\&B) algorithm to the D-optimality problem based on a convex mixed-integer nonlinear formulation. We discuss possible methodologies to accelerate the convergence of the B\&B algorithm, by combining the use of…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
By forcing at most N out of M consecutive weights to be non-zero, the recent N:M network sparsity has received increasing attention for its two attractive advantages: 1) Promising performance at a high sparsity. 2) Significant speedups on…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
A big challenge in branch and bound lies in identifying the optimal node within the search tree from which to proceed. Current state-of-the-art selectors utilize either hand-crafted ensembles that automatically switch between naive sub-node…