Submodular functions are a broad class of set functions, which naturally arise in diverse areas such as economics, operations research and game theory. Many algorithms have been suggested for the maximization of these functions, achieving both strong theoretical guarantees and good practical performance. Unfortunately, once the function deviates from submodularity (even slightly), the known alg...

We consider the problem of maximizing a nonmonotone DR-submodular function subject to a cardinality constraint. Diminishing returns (DR) submodularity is a generalization of the diminishing returns property for functions defined over the integer lattice. This generalization can be used to solve many machine learning or combinatorial optimization problems such as optimal budget allocation, reven...

We describe how the propagator for the All-Different constraint can be generalized to prune variables whose domains are not just simple finite integer domains. We show, for example, how it can be used to propagate set, multiset and tuple variables.

Software factories have been proposed as a comprehensive and integrative approach to generative software development. Feature modeling has several applications in generative software development, including domain analysis, product-line scoping, and feature-based product specification. This paper reports on our recent progress in cardinalitybased feature modeling and its support for expressing a...

The bin-packing problem asks for a packing of a list of items of sizes from (0; 1] into the smallest possible number of bins having unit capacity. The k-item bin-packing problem additionally imposes the constraint that at most k items are allowed in one bin. We present two e6cient on-line algorithms for this problem. We show that, for increasing values of k, the bound on the asymptotic worst-ca...

We show how to generate randomized roundings of rational vectors that satisfy hard cardinality constraints and allow large deviations bounds. This improves and extends earlier results by Srinivasan (FOCS 2001), Gandhi et al. (FOCS 2002) and the author (STACS 2006). Roughly speaking, we show that also for rounding arbitrary rational vectors randomly or deterministically, it suffices to understan...

Conceptual modelling formalisms such as the Entity-Relationship model (ER) and Unified Modelling Language (UML) have become a de facto standard in database design by providing visual means to describe application domains in a declarative and reusable way. On the other hand, both ER and UML turned out to be closely connected with description logics that are underpinned by formal semantics and th...

A variation of preemptive open shop scheduling corresponds to nding a feasible edge coloring in a bipartite multigraph with some requirements on the size of the di erent color classes. We show that for trees with xed maximum degree, one can nd in polynomial time an edge k-coloring where for i = 1; : : : ; k the number of edges of color i is exactly a given number hi, and each edge e gets its co...

We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardi-nality atoms to the language of propositional logic facilitates modeling search problems and often results in concise encodings. We propose two " native " local-search solvers for theorie...

Cardinality constraints enforce an upper bound on the number of variables that can be nonzero. This article investigates linear programs with cardinality constraints that mutually overlap, i.e., share variables. We present the components of a branch-and-cut solution approach, including new branching rules that exploit the structure of the corresponding conflict hypergraph. We also investigate v...