Tight Approximation Algorithms for Scheduling with Fixed Jobs and Non-Availability

We study two closely related problems in non-preemptive scheduling of sequential jobs on identical parallel machines. In these two settings there are either fixed jobs or non-availability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, e.g. in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of $3/2+\epsilon$, respectively, which we refine to approximation algorithms with ratio $3/2$. For scheduling with fixed jobs, a lower bound of $3/2$ on the approximation ratio has been obtained by Scharbrodt, Steger & Weisser: for scheduling with non-availability we provide the same lower bound. In total, our approximation ratio for both problems is tight via suitable inapproximability results. We use dual approximation, creation of a gap structure and job configurations, and a PTAS for the multiple subset sum problem. However, the main feature of our algorithms is a new technique for the assignment of large jobs via flexible rounding. Our new technique is based on an interesting cyclic shifting argument in combination with a network flow model for the assignment of jobs to large gaps

Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows

We present heuristics to handle practical travelling salesman problems with multiple time windows per node, where the optimization goal is minimal tour duration, which is the time spent outside the depot node. We propose a dynamic programming approach which combines state labels by encoding intervals to handle the larger state space needed for this objective function. Our implementation is able to solve many practical instances in real-time and is used for heuristic search of near-optimal solutions for hard instances. In addition, we outline a hybrid genetic algorithm we implemented to cope with hard or unknown instances. Experimental evaluation proves the efficiency and suitability for practical use of our algorithms and even leads to improved upper bounds for yet unsolved instances from the literature

Algorithmes d'approximation pour des programmes linéaires et les problèmes de Packing avec des contraintes géometriques

In this thesis we approach several problems with approximation algorithms; these are feasibility problems as well as optimization problems. In Chapter 1 we give a brief introduction into the general paradigm of approximation algorithms, motivate the problems, and give an outline of the thesis. In Chapter 2, we discuss two algorithms to approximately generate a feasible solution of the mixed packing and covering problem which is a model from convex optimization. This problem includes a large class of linear programs. The algorithms generate approximately feasible solutions within O(M(ln M+epsilon^{-2} ln epsilon^{-1})) and O(M epsilon{-2} ln (M epsilon^{-1}))$iterations, respectively, where in each iteration a block problem which depends on the specific application has to be solved. Both algorithms, applied to linear programs, can result in column generation algorithms. In Chapter 3, we implement an algorithm for the so-called max-min-resource sharing problem. This is a certain convex optimization problem which, similar to the problem in Chapter 1, includes a large class of linear programs. The implementation, which is included in the appendix, is done in C++. We use the implementation in the context of an AFPTAS for Strip Packing in order to evaluate dynamic optimization of a parameter in the algorithm, namely the step length used for interpolation. We compare our choice to the static step length proposed in the analysis of the algorithm and conclude that dynamic optimization of the step length significantly reduces the number of iterations. In Chapter 4, we study two closely related scheduling problems, namely non-preemptive scheduling with fixed jobs and scheduling with non-availability for sequential jobs on m identical machines under the makespan objective, where m is constant. For the first problem, which does not admit an FPTAS unless P=NP, we obtain a new PTAS. For the second problem, we show that a suitable restriction (namely the permanent availability of one machine) is necessary to obtain a bounded approximation ratio. For this restriction, which does not admit an FPTAS unless P=NP, we present a PTAS; we also discuss the complexity of various special cases. In total, the results are basically best possible. In Chapter 5, we continue the studies from Chapter 4 where now the number m of machines is part of the input, which makes the problem algorithmically harder. Scheduling with fixed jobs does not admit an approximation ratio better than 3/2, unless P=NP; here we obtain an approximation ratio of 3/2+epsilon for any epsilon>0. For scheduling with non-availability, we require a constant percentage of the machines to be permanently available. This restriction also does not admit an approximation ratio better than 3/2 unless P=NP; we also obtain an approximation ratio of$3/2+\epsilon$ for any epsilon>0. With an interesting argument, the approximation ratio for both problems is refined to exactly 3/2. We also point out an interesting relation of scheduling with fixed jobs to Bin Packing. As in Chapter 4, the results are in a certain sense best possible. Finally, in Chapter 6, we conclude with some remarks and open research problems

Algorithmes d'approximation pour des programmes linéaires et les problèmes de Packing avec des contraintes géometriques

In this thesis we approach several problems with approximation algorithms; these are feasibility problems as well as optimization problems. In Chapter 1 we give a brief introduction into the general paradigm of approximation algorithms, motivate the problems, and give an outline of the thesis. In Chapter 2, we discuss two algorithms to approximately generate a feasible solution of the mixed packing and covering problem which is a model from convex optimization. This problem includes a large class of linear programs. The algorithms generate approximately feasible solutions within O(M(ln M+epsilon^{-2} ln epsilon^{-1})) and O(M epsilon{-2} ln (M epsilon^{-1}))$iterations, respectively, where in each iteration a block problem which depends on the specific application has to be solved. Both algorithms, applied to linear programs, can result in column generation algorithms. In Chapter 3, we implement an algorithm for the so-called max-min-resource sharing problem. This is a certain convex optimization problem which, similar to the problem in Chapter 1, includes a large class of linear programs. The implementation, which is included in the appendix, is done in C++. We use the implementation in the context of an AFPTAS for Strip Packing in order to evaluate dynamic optimization of a parameter in the algorithm, namely the step length used for interpolation. We compare our choice to the static step length proposed in the analysis of the algorithm and conclude that dynamic optimization of the step length significantly reduces the number of iterations. In Chapter 4, we study two closely related scheduling problems, namely non-preemptive scheduling with fixed jobs and scheduling with non-availability for sequential jobs on m identical machines under the makespan objective, where m is constant. For the first problem, which does not admit an FPTAS unless P=NP, we obtain a new PTAS. For the second problem, we show that a suitable restriction (namely the permanent availability of one machine) is necessary to obtain a bounded approximation ratio. For this restriction, which does not admit an FPTAS unless P=NP, we present a PTAS; we also discuss the complexity of various special cases. In total, the results are basically best possible. In Chapter 5, we continue the studies from Chapter 4 where now the number m of machines is part of the input, which makes the problem algorithmically harder. Scheduling with fixed jobs does not admit an approximation ratio better than 3/2, unless P=NP; here we obtain an approximation ratio of 3/2+epsilon for any epsilon>0. For scheduling with non-availability, we require a constant percentage of the machines to be permanently available. This restriction also does not admit an approximation ratio better than 3/2 unless P=NP; we also obtain an approximation ratio of$3/2+\epsilon$ for any epsilon>0. With an interesting argument, the approximation ratio for both problems is refined to exactly 3/2. We also point out an interesting relation of scheduling with fixed jobs to Bin Packing. As in Chapter 4, the results are in a certain sense best possible. Finally, in Chapter 6, we conclude with some remarks and open research problems

Tight Approximation Algorithms for Scheduling with Fixed Jobs and Non-Availability

We study two closely related problems in non-preemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or non-availability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, e.g. in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt, Steger & Weisser; for scheduling with non-availability we provide the same lower bound. We use dual approximation, creation of a gap structure and a PTAS for the multiple subset sum problem, combined with a post- processing step to assign large job

Retromer- and WASH-dependent sorting of nutrient transporters requires a multivalent interaction network with ANKRD50

Retromer and the associated actin-polymerizing WASH complex are essential for the endocytic recycling of a wide range of integral membrane proteins. A hereditary Parkinson's-disease-causing point mutation (D620N) in the retromer subunit VPS35 perturbs retromer's association with the WASH complex and also with the uncharacterized protein ankyrin-repeat-domain-containing protein 50 (ANKRD50). Here, we firmly establish ANKRD50 as a new and essential component of the SNX27– retromer–WASH super complex. Depletion of ANKRD50 in HeLa or U2OS cells phenocopied the loss of endosome-to-cell-surface recycling of multiple transmembrane proteins seen upon suppression of SNX27, retromer or WASH- complex components. Mass-spectrometry-based quantification of the cell surface proteome of ANKRD50-depleted cells identified amino acid transporters of the SLC1A family, among them SLC1A4, as additional cargo molecules that depend on ANKRD50 and retromer for their endocytic recycling. Mechanistically, we show that ANKRD50 simultaneously engages multiple parts of the SNX27–retromer–WASH complex machinery in a direct and co-operative interaction network that is needed to efficiently recycle the nutrient transporters GLUT1 (also known as SLC2A1) and SLC1A4, and potentially many other surface proteins

Retromer/WASH dependent sorting of nutrient transporters requires a multivalent interaction network with ANKRD50

Retromer and the associated actin-polymerizing WASH complex are essential for the endocytic recycling of a wide range of integral membrane proteins. A hereditary Parkinson's-disease-causing point mutation (D620N) in the retromer subunit VPS35 perturbs retromer's association with the WASH complex and also with the uncharacterized protein ankyrin-repeat-domain-containing protein 50 (ANKRD50). Here, we firmly establish ANKRD50 as a new and essential component of the SNX27–retromer–WASH super complex. Depletion of ANKRD50 in HeLa or U2OS cells phenocopied the loss of endosome-to-cell-surface recycling of multiple transmembrane proteins seen upon suppression of SNX27, retromer or WASH-complex components. Mass-spectrometry-based quantification of the cell surface proteome of ANKRD50-depleted cells identified amino acid transporters of the SLC1A family, among them SLC1A4, as additional cargo molecules that depend on ANKRD50 and retromer for their endocytic recycling. Mechanistically, we show that ANKRD50 simultaneously engages multiple parts of the SNX27–retromer–WASH complex machinery in a direct and co-operative interaction network that is needed to efficiently recycle the nutrient transporters GLUT1 (also known as SLC2A1) and SLC1A4, and potentially many other surface proteins

Phospho-proteomic analyses of B-Raf protein complexes reveal new regulatory principles

B-Raf represents a critical physiological regulator of the Ras/RAF/MEK/ERK-pathway and a pharmacological target of growing clinical relevance, in particular in oncology. To understand how B-Raf itself is regulated, we combined mass spectrometry with genetic approaches to map its interactome in MCF-10A cells as well as in B-Raf deficient murine embryonic fibroblasts (MEFs) and B-Raf/Raf-1 double deficient DT40 lymphoma cells complemented with wildtype or mutant B-Raf expression vectors. Using a multi-protease digestion approach, we identified a novel ubiquitination site and provide a detailed B-Raf phospho-map. Importantly, we identify two evolutionary conserved phosphorylation clusters around T401 and S419 in the B-Raf hinge region. SILAC labelling and genetic/biochemical follow-up revealed that these clusters are phosphorylated in the contexts of oncogenic Ras, sorafenib induced Raf dimerization and in the background of the V600E mutation. We further show that the vemurafenib sensitive phosphorylation of the T401 cluster occurs in trans within a Raf dimer. Substitution of the Ser/Thr-residues of this cluster by alanine residues enhances the transforming potential of B-Raf, indicating that these phosphorylation sites suppress its signaling output. Moreover, several B-Raf phosphorylation sites, including T401 and S419, are somatically mutated in tumors, further illustrating the importance of phosphorylation for the regulation of this kinase

Mast Cells Trigger Disturbed Bone Healing in Osteoporotic Mice

ABSTRACT Mast cells are important tissue‐resident sensor and effector immune cells but also play a major role in osteoporosis development. Mast cells are increased in numbers in the bone marrow of postmenopausal osteoporotic patients, and mast cell–deficient mice are protected from ovariectomy (OVX)‐induced bone loss. In this study, we showed that mast cell–deficient Mcpt5‐Cre R‐DTA mice were protected from OVX‐induced disturbed fracture healing, indicating a critical role for mast cells in the pathomechanisms of impaired bone repair under estrogen‐deficient conditions. We revealed that mast cells trigger the fracture‐induced inflammatory response by releasing inflammatory mediators, including interleukin‐6, midkine (Mdk), and C‐X‐C motif chemokine ligand 10 (CXCL10), and promote neutrophil infiltration into the fracture site in OVX mice. Furthermore, mast cells were responsible for reduced osteoblast and increased osteoclast activities in OVX mice callus, as well as increased receptor activator of NF‐κB ligand serum levels in OVX mice. Additional in vitro studies with human cells showed that mast cells stimulate osteoclastogenesis by releasing the osteoclastogenic mediators Mdk and CXCL10 in an estrogen‐dependent manner, which was mediated via the estrogen receptor alpha on mast cells. In conclusion, mast cells negatively affect the healing of bone fractures under estrogen‐deficient conditions. Hence, targeting mast cells might provide a therapeutic strategy to improve disturbed bone repair in postmenopausal osteoporosis. © 2021 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR)

In vivo imaging of pancreatic tumours and liver metastases using 7 Tesla MRI in a murine orthotopic pancreatic cancer model and a liver metastases model

<p>Abstract</p> <p>Background</p> <p>Pancreatic cancer is the fourth leading cause of tumour death in the western world. However, appropriate tumour models are scarce. Here we present a syngeneic murine pancreatic cancer model using 7 Tesla MRI and evaluate its clinical relevance and applicability.</p> <p>Methods</p> <p>6606PDA murine pancreatic cancer cells were orthotopically injected into the pancreatic head. Liver metastases were induced through splenic injection. Animals were analyzed by MRI three and five weeks following injection. Tumours were detected using T2-weighted high resolution sequences. Tumour volumes were determined by callipers and MRI. Liver metastases were analyzed using gadolinium-EOB-DTPA and T1-weighted 3D-Flash sequences. Tumour blood flow was measured using low molecular gadobutrol and high molecular gadolinium-DTPA.</p> <p>Results</p> <p>MRI handling and applicability was similar to human systems, resolution as low as 0.1 mm. After 5 weeks tumour volumes differed significantly (p < 0.01) when comparing calliper measurments (n = 5, mean 1065 mm³+/-243 mm³) with MRI (mean 918 mm³+/-193 mm³) with MRI being more precise. Histology (n = 5) confirmed MRI tumour measurements (mean size MRI 38.5 mm²+/-22.8 mm²versus 32.6 mm²+/-22.6 mm²(histology), p < 0,0004) with differences due to fixation and processing of specimens. After splenic injection all mice developed liver metastases with a mean of 8 metastases and a mean volume of 173.8 mm³+/-56.7 mm³after 5 weeks. Lymphnodes were also easily identified. Tumour accumulation of gadobutrol was significantly (p < 0.05) higher than gadolinium-DTPA. All imaging experiments could be done repeatedly to comply with the 3R-principle thus reducing the number of experimental animals.</p> <p>Conclusions</p> <p>This model permits monitoring of tumour growth and metastasis formation in longitudinal non-invasive high-resolution MR studies including using contrast agents comparable to human pancreatic cancer. This multidisciplinary environment enables radiologists, surgeons and physicians to further improve translational research and therapies of pancreatic cancer.</p