Related papers: An Experimental Study of ILP Formulations for the …
The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…
Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
While finding a path between two nodes is the basis for several applications, the need for alternative paths also may have various motivations. For instance, this can be of interest for ensuring reliability in a telecommunications network,…
${ NP}$-complete problem "Hamiltonian cycle"\ for graph $G=(V,E)$ is extended to the "Hamiltonian Complement of the Graph"\ problem of finding the minimal cardinality set $H$ containing additional edges so that graph $G=(V,E\cup H)$ is…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
In the Model-Driven Software Engineering (MDSE) community, the combination of techniques operating on graph-based models (e.g., Pattern Matching (PM) and Graph Transformation (GT)) and Integer Linear Programming (ILP) is a common…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We…
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…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
Graphs have been commonly used to model many applications. A natural problem which abstracts applications such as itinerary planning, playlist recommendation, and flow analysis in information networks is that of finding the heaviest path(s)…
A graph $G$ is called $B_k$-VPG, for some constant $k\geq 0$, if it has a string representation on an axis-parallel grid such that each vertex is a path with at most $k$ bends and two vertices are adjacent in $G$ if and only if the…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
The Mapper produces a compact summary of high dimensional data as a simplicial complex. We study the problem of quantifying the interestingness of subpopulations in a Mapper, which appear as long paths, flares, or loops. First, we create a…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Link weights are the principal parameters of shortest path routing protocols, the most commonly used protocols for IP networks. The problem of optimally setting link weights for unique shortest path routing is addressed. Due to the…