The Valued Constraint Satisfaction Problem (VCSP) is a general framework encompassing many optimisation problems. We discuss precisely what it means for a problem to be modelled in the VCSP framework. Using our analysis, we show that some optimisation problems, such as (s, t)-Min-Cut and Submodular Function Minimisation, can be modelled using a restricted set of valued constraints which are tra...

For a given polygonal chain and a family of tolerance regions, we study the min-# problem, which consists in finding an approximate and ordered subchain with a minimum number of vertices. Our algorithm computes an approximation that retains the shape of the original chain. Moreover, our method reaches a near-linear time complexity and its implementation is based on classical functions. To our k...

We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by Õ(m3/2). This matches the best known bounds, which previously have only been achieved by numerical algorithms or for special cases. Our contribution contains three parts that might be interesting in their own right: (1) We provide a construction of an equivalent auxiliary netwo...

A variety of problems in non-linear time-evolution systems such as manufacturing plants, operations research, computer networks, etc., can be modelled as min-max-plus systems in which operations of min, max and addition appear simultaneously. It is well know that systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes t...

The min-max Split Delivery Multi-Depot Vehicle Routing Problem with Minimum Service Time Requirement (min-max SDMDVRP-MSTR) is a variant of the Multi-Depot Vehicle Routing Problem. Each customer requires a specified amount of service time. The service time can be split among vehicles as long as each vehicle spends a minimum amount of service time at a customer. The objective is to minimize the ...

Multicast sessions may have a large number of receivers with heterogeneous reception capacities. To accommodate this heterogeneity, various multi-rate schemes, based upon the use of layering or replication, have been proposed. We consider in this paper the optimal partitioning of receivers into groups for multi-rate schemes. For a general class of utility functions, we formulate the partitionin...

the location-routing problem is a relatively new branch of logistics system. its objective is to determine a suitable location for constructing distribution warehouses and proper transportation routing from warehouse to the customer. in this study, the location-routing problem is investigated with considering fuzzy servicing time window for each customer. another important issue in this regard ...