Search and test algorithms for Triple Product Property triples

In 2003 COHN and UMANS introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group $G$ satisfying the Triple Product Property (TPP) as a means to bound the exponent $\omega$ of matrix multiplication. We present two new characterizations of the TPP, which are useful for theoretical considerations and for TPP test algorithms. With this we describe all known TPP tests and implement them in GAP algorithms. We also compare their runtime. Furthermore we show that the search for subgroup TPP triples of nontrivial size in a nonabelian group can be restricted to the set of all nonnormal subgroups of that group. Finally we describe brute-force search algorithms for maximal subgroup and subset TPP triples. In addition we present the results of the subset brute-force search for all groups of order less than 25 and selected results of the subgroup brute-force search for 2-groups, $SL(n,q)$ and $PSL(2,q)$.Comment: 14 pages, 2 figures, 4 tables; ISSN (Online) 1869-6104, ISSN (Print) 1867-114

Exact Algorithms for the Maximum Planar Subgraph Problem: New Models and Experiments

Given a graph G, the NP-hard Maximum Planar Subgraph problem asks for a planar subgraph of G with the maximum number of edges. The only known non-trivial exact algorithm utilizes Kuratowski\u27s famous planarity criterion and can be formulated as an integer linear program (ILP) or a pseudo-boolean satisfiability problem (PBS). We examine three alternative characterizations of planarity regarding their applicability to model maximum planar subgraphs. For each, we consider both ILP and PBS variants, investigate diverse formulation aspects, and evaluate their practical performance

Spot Market versus Full Charter Fleet:Decisions Support for Full Truck Load Tenders

This paper presents an approach to help business decision-makers gain market share by providing competitive tender offers for Full-Truck-Load (FTL) services. In particular, we compare operating a fleet of Full-Charter-Trucks (FCT), using spot-market (SM) capacity and a mixture of both options against each other. A Pickup and Delivery Problem is modeled, and solved using an Adaptive Large Neighborhood Search heuristic. Computational results indicate strong service benefits combining FCT and SM usage. Numerical experiments are presented in detail to support the findings. Additionally, a real-life case study originating from DB Schenker is presented.Comment: 22 pages, 4 figures, 9 table

Partitioned vs. Integrated Planning of Hinterland Networks for LCL Transportation

Utilizing existing transportation networks better and designing (parts of) networks involves routing decisions to minimize transportation costs and maximize consolidation effects. We study the concrete example of hinterland networks for the truck-transportation of less-than-container-load (LCL) ocean freight shipments: A set of LCL shipments is given. They have to be routed through the hinterland network to be transported to an origin port and finally to the destination port via ship. On their way, they can be consolidated in hubs to full-container-load (FCL) shipments. The overall transportation cost depends on the selection of the origin port and the routing and consolidation in the hinterland network. A problem of this type appears for the global logistics provider DB Schenker. We translate the business problem into a hub location problem, describe it mathematically, and discuss solution strategies. As a result, an integrated modeling approach has several advantages over solving a simplified version of the problem, although it requires more computational effort