Related papers: Integer Programming Models and Parameterized Algor…
In this paper, the cooperative caching problem in fog radio access networks (F-RAN) is investigated. To maximize the incremental offloaded traffic, we formulate the clustering optimization problem with the consideration of cooperative…
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical…
Some airlines use the preferential bidding system to construct the schedules of their pilots. In this system, the pilots bid on the different activities and the schedules that lexicographically maximize the scores of the pilots according to…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
We present an Integer Linear Programming based approach to finding the optimal fusion strategy for combinator-based parallel programs. While combinator-based languages or libraries provide a convenient interface for programming parallel…
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
Powerful results from the theory of integer programming have recently led to substantial advances in parameterized complexity. However, our perception is that, except for Lenstra's algorithm for solving integer linear programming in fixed…
Order picking is the process of retrieving ordered products from storage locations in warehouses. In picker-to-parts order picking systems, two or more customer orders may be grouped and assigned to a single picker. Then routing decision…
An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into \emph{bundles}. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between…
We consider integer programs whose constraint matrix has a special block structure: $\min\{f(x):H_{com}x=b, l\le x\le u,x\in\mathbb{Z}^{t_B+nt_A}\}$, where the objective function $f$ is separable convex and the constraint matrix $H_ {com}$…
Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel…
Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output label space. These constraints interact with the learned models to filter infeasible…
The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. While several mixed integer programming (MIP)…
Lifting is a crucial technique in mixed integer programming (MIP) for generating strong valid inequalities, which serve as cutting planes to improve the branch-and-cut algorithm. We first propose an exact sequential lifting algorithm for…