Related papers: Exact Decomposition Branching exploiting Lattice S…
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…
We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
Works on implicit regularization have studied gradient trajectories during the optimization process to explain why deep networks favor certain kinds of solutions over others. In deep linear networks, it has been shown that gradient descent…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an $s$-dimensional integral is fully specified by its generating vector $\mathbf{z}…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
The irregular strip-packing problem consists of the computation of a non-overlapping placement of a set of polygons onto a rectangular strip of fixed width and the minimal length possible. Recent performance gains of the Mixed-Integer…
New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules.
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…