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We generalize the classical nuts and bolts problem to a setting where the input is a collection of $n$ nuts and $m$ bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and webpages. In this paper, we study the problem of ranking vertices of a bipartite graph,…
The linearized Bregman iterations (LBreI) and its variants have received considerable attention in signal/image processing and compressed sensing. Recently, LBreI has been extended to a larger class of nonconvex functions, along with…
We present a quasi linear-time algorithm for Maximum Matching on distance-hereditary graphs and some of their generalizations. This improves on [Dragan, WG'97], who proposed such an algorithm for the subclass of (tent,hexahedron)-free…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
Given a digraph $G = (V_G, A_G)$, a \emph{branching} in $G$ is a set of arcs $B \subseteq A_G$ such that the underlying undirected graph spanned by $B$ is acyclic and each node in $G$ is entered (\emph{covered}) by at most one arc from $B$.…
The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded…
In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node…
We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are…
Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
One of the challenges of cloud computing is to optimally and efficiently assign virtual ma- chines to physical machines. The aim of telecommunication operators is to minimize the map- ping cost while respecting constraints regarding…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
Dense subgraph discovery is an important problem in graph mining and network analysis with several applications. Two canonical problems here are to find a maxcore (subgraph of maximum min degree) and to find a densest subgraph (subgraph of…
Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We…