Sequential and Parallel Algorithms for Mixed Packing and Covering

Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set cover, bin-packing, knapsack, scheduling problems, minimum-weight triangulation, etc. This paper gives approximation algorithms for the general class of problems. The sequential algorithm is a simple greedy algorithm that can be implemented to find an epsilon-approximate solution in O(epsilon^-2 log m) linear-time iterations. The parallel algorithm does comparable work but finishes in polylogarithmic time. The results generalize previous work on pure packing and covering (the special case when the constraints are all "less-than" or all "greater-than") by Michael Luby and Noam Nisan (1993) and Naveen Garg and Jochen Konemann (1998)

Generalized Markov stability of network communities

We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The specific implementation of the quality function and the resulting optimal community structure thus become dependent both on the type of Markov process and on the specific Markov times considered. For instance, if we use a natural Markov chain dynamics and discount its stationary distribution -- that is, we take as reference process the dynamics at infinite time -- we obtain the standard formulation of the Markov stability. Notably, the possibility to use finite-time transition probabilities to define the reference process naturally allows detecting communities at different resolutions, without the need to consider a continuous-time Markov chain in the small time limit. The main advantage of our general formulation of Markov stability based on dynamical flows is that we work with lumped Markov chains on network partitions, having the same stationary distribution of the original process. In this way the form of the quality function becomes invariant under partitioning, leading to a self-consistent definition of community structures at different aggregation scales

A Business Process Management System based on a General Optimium Criterion

Business Process Management Systems (BPMS) provide a broad range of facilities to manage operational business processes. These systems should provide support for the complete Business Process Management (BPM) life-cycle (16): (re)design, configuration, execution, control, and diagnosis of processes. BPMS can be seen as successors of Workflow Management (WFM) systems. However, already in the seventies people were working on office automation systems which are comparable with today’s WFM systems. Recently, WFM vendors started to position their systems as BPMS. Our paper’s goal is a proposal for a Tasks-to-Workstations Assignment Algorithm (TWAA) for assembly lines which is a special implementation of a stochastic descent technique, in the context of BPMS, especially at the control level. Both cases, single and mixed-model, are treated. For a family of product models having the same generic structure, the mixed-model assignment problem can be formulated through an equivalent single-model problem. A general optimum criterion is considered. As the assembly line balancing, this kind of optimisation problem leads to a graph partitioning problem meeting precedence and feasibility constraints. The proposed definition for the "neighbourhood" function involves an efficient way for treating the partition and precedence constraints. Moreover, the Stochastic Descent Technique (SDT) allows an implicit treatment of the feasibility constraint. The proposed algorithm converges with probability 1 to an optimal solution.BPMS, control assembly system, stochastic optimisation techniques, TWAA, SDT