Related papers: Thinner is not Always Better: Cascade Knapsack Pro…
One of the important unsolved problems in information theory is the conjecture that network coding has no rate benefit over routing in undirected unicast networks. Three known bounds on the symmetric rate in undirected unicast information…
The cable-trench problem is defined as a linear combination of the shortest path and the minimum spanning tree problem. In particular, the goal is to find a spanning tree that simultaneously minimizes its total length and the total path…
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…
Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs…
One model of message delivery in a computer network is based on labelling each edge by a subset of a (reasonably small) universal set, and then encoding a path as the union of the labels of its edges. Earlier work suggested using random…
Segment Routing is a recent network technology that helps optimizing network throughput by providing finer control over the routing paths. Instead of routing directly from a source to a target, packets are routed via intermediate waypoints.…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
A thin tube is an $n$-dimensional space which is very thin in $n-1$ directions, compared to the remaining direction, for example the $\epsilon$-neighborhood of a curve or an embedded graph in $\R^n$ for small $\epsilon$. The Laplacian on…
We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed…
The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…
Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output…
Minimum Bisection denotes the NP-hard problem to partition the vertex set of a graph into two sets of equal sizes while minimizing the width of the bisection, which is defined as the number of edges between these two sets. We first consider…
Batched network coding (BNC) is a solution to multi-hop transmission on networks with packet loss. To be compatible with the existing infrastructure, BNC is usually implemented over UDP. A single error bit will probably result in discarding…