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Tracking Interacting Objects Optimally Using Integer Programming

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Multiple Object Tracking using Flow Linear Programming

Pascal Fua, François Fleuret, Jérôme Berclaz

Multi-object tracking can be achieved by detecting objects in individ- ual frames and then linking detections across frames. Such an approach can be made very robust to the occasional detection failure: If an object is not detected in a frame but is in pre ...

Idiap2009

Network Formulations of Mixed-Integer Programs

Friedrich Eisenbrand, Marco Di Summa

We consider mixed-integer sets described by system of linear inequalities in which the constraint matrix A is totally unimodular; the right-hand side is arbitrary vector; and a subset of the variables is required to be integer. We show that the problem of ...

INFORMS2009

Branch and Price for the Vehicle Routing Problem with Discrete Split Deliveries and Time Windows

Matteo Salani, Ilaria Vacca

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles capacity and customer time windows. ...

2009

Parametric integer programming in fixed dimension

Friedrich Eisenbrand, Gennady Shmonin

We consider the following problem: Given a rational matrix

A \in \mathbb{Q}^{m \times n}

and a rational polyhedron

Q \subseteq \mathbb{R}^{m+p}

, decide if for all vectors

b \in \mathbb{R}^m

, for which there exists an integral

z \in \mathbb{Z}^p

suc ...

2008

Mapping task-graphs on distributed ECU networks: Efficient algorithms for feasibility and optimality

Friedrich Eisenbrand, Gennady Shmonin

This mapping problem has to be solved in many application scenarios. In the automotive industry, for example, the implementation of car functions involves distributed task sets running on multiple electronic control units (ECU) with bus-based inter-task co ...

2006

Caratheodory bounds for integer cones

Friedrich Eisenbrand, Gennady Shmonin

We provide analogues of Caratheodory's theorem for integer cones and apply our bounds to integer programming and to the cutting stock problem. In particular, we provide an NP certificate for the latter, whose existence has not been known so far. © 2005 Els ...

2006

On the complexity of integer programming in fixed dimension

Friedrich Eisenbrand

Summary form only given. Integer programming is the problem of maximizing a linear function over the integer vectors which satisfy a given set of inequalities. A wide range of combinatorial optimization problems can be modeled as integer programming proble ...

2005

A linear algorithm for integer programming in the plane

Friedrich Eisenbrand

We show that a 2-variable integer program, defined by m constraints involving coefficients with at most φ bits, can be solved with O(m+φ) arithmetic operations on rational numbers of size O(φ). © Springer-Verlag 2004. ...

2005

Networked Slepian-Wolf: Theory and Algorithms

Martin Vetterli, Razvan Cristescu

In this paper, we consider the minimization of a relevant energy consumption related cost function in the context of sensor networks where correlated sources are generated at various sets of source nodes and have to be transmitted to some set of sink nodes ...

Springer Verlag2004

Networked Slepian-Wolf: Theory and Algorithms

Martin Vetterli, Razvan Cristescu

2004

Parametric integer programming in fixed dimension

Friedrich Eisenbrand, Gennady Shmonin

We consider the following problem: Given a rational matrix

A \in \mathbb{Q}^{m \times n}

and a rational polyhedron

Q \subseteq \mathbb{R}^{m+p}

, decide if for all vectors

b \in \mathbb{R}^m

, for which there exists an integral

z \in \mathbb{Z}^p

suc ...

2008