Intersection Graphs in Simultaneous Embedding with Fixed Edges

We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their in- tersection S := G1 ∩ G2 . In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1 , G2 ). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pair of pla- nar graphs (G1 , G2 ) with intersection S = G1 ∩ G2 has a simultaneous embedding with fixed edges. We will characterize this set by a detailed study of topological embeddings and finally give a complete list of graphs in this set as our main result of this paper

Intersection Graphs in Simultaneous Embedding with Fixed Edges

We examine the simultaneous embedding with ?xed edges problem for two planar graphs G1 and G2 with the focus on their in- tersection S := G1 ? G2 . In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with ?xed edges for (G1 , G2 ). More formally, we de?ne the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pair of pla- nar graphs (G1 , G2 ) with intersection S = G1 ? G2 has a simultaneous embedding with ?xed edges. We will characterize this set by a detailed study of topological embeddings and ?nally give a complete list of graphs in this set as our main result of this paper

Large-Graph Layout with the Fast Multipole Multilevel Method

The visualization of of large and complex networks or graphs is an indispensable instrument for getting deeper insight into their structure. Force-directed graph-drawing algorithms are widely used to draw such graphs. However, these methods do not guarantee a sub-quadratic running time in general. We present a new force-directed method that is based on a combination of an efficient multilevel scheme and a strategy for approximating the repulsive forces in the system by rapidly evaluating potential fields. Given a graph G=(V,E), the asymptotic worst-case running time of this method is O(|V|log|V|+|E|) with linear memory requirements. In practice, the algorithm generates nice drawings of graphs with 100000 nodes in less than 5 minutes. Furthermore, it clearly visualizes even the structures of those graphs that turned out to be challenging for other methods

Solving the Simple Offset Assignment Problem as a Traveling Salesman

In this paper, we present an exact approach to the Simple Offset Assignment problem arising in the domain of address code generation for digital signal processors. It is based on transformations to weighted Hamiltonian cycle problems and integer linear programming. To the best of our knowledge, it is the first approach capable to solve all instances of the established OffsetStone benchmark set to optimality within reasonable time. Therefore, it enables to evaluate the quality of several heuristics relative to the optimum solutions for the first time. Further, using the same transformations, we present a simple and effective improvement heuristic. In addition, we include an existing heuristic into our experiments that has so far not been evaluated with OffsetStone

Linear Optimization over Permutation Groups

For a permutation group given by a set of generators, the problem of finding "special" group members is NP-hard in many cases. E.g., this is true for the problem of finding a permutation with a minimum number of fixed points or a permutation with a minimal Hamming distance from a given permutation. Many of these problems can be modeled as linear optimization problems over permutation groups. We develop a polyhedral approach to this general problem and derive an exact and practically fast algorithm based on the branch&cut-technique

Solving large-scale traveling salesman problems with parallel Branch-and-Cut

We introduce the implementation of a parallel Branch-and-Cut algorithm to solve large-scale traveling salesman problems. Rather than using the well-known models of homogeneous distribution and simple Master/Slave communication, we present a more sophisticated distribution that takes the advantage of several independent features of a Branch-and-Cut code. Computational results are reported for several instances of the TSPLIB

An Integer Programming Approach to Optimal Basic Block Instruction Scheduling for Single-Issue Processors

We present a novel integer programming formulation for basic block instruction scheduling on single-issue processors. The problem can be considered as a very general sequential task scheduling problem with delayed precedence-constraints. Our model is based on the linear ordering problem and has, in contrast to the last IP model proposed, numbers of variables and constraints that are strongly polynomial in the instance size. Combined with improved preprocessing techniques and given a time limit of ten minutes of CPU and system time, our branch-and-cut implementation is capable to solve all but eleven of the 369,861 basic blocks of the SPEC 2000 integer and floating point benchmarks to proven optimality. This is competitive to the current state-of-the art constraint programming approach that has also been evaluated on this test suite

GEODUAL: Fun with Geometric Duality

We present GEODUAL, a software for creating and solving geometric instances of the Minimum Spanning Tree problem, the Perfect Matching problem, and the Traveling Salesman problem, along with visual proofs of optimality

The QAP-Polytope and the Star-Transformation

Polyhedral Combinatorics has been successfully applied to obtain considerable algorithmic progress towards the solution of many prominent hard combinatorial optimization problems. Until very recently, the quadratic assignment problem (QAP) was one of the few exceptions. Recent work of Rijal (1995) and Padberg and Rijal (1996) has on the one hand yielded some basic facts about the associated quadratic assignment polytope, but has on the other hand shown that investigations even of the very basic questions (like the dimension, the affine hull, and the trivial facets) soon become extremely complicated. In this paper, we propose an isomorphic transformation of the ''natural'' realization of the quadratic assignment polytope, which simplifies the polyhedral investigations enormously. We demonstrate this by giving short proofs of the basic results on the polytope that indicate that, exploiting the techniques developed in this paper, deeper polyhedral investigations of the QAP now become possible. Moreover, an 'ìnductive construction'' of the QAP-Polytope is derived that might be useful in branch-and-cut algorithms