The knapsack problem with special neighbor constraints

The knapsack problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two knapsack problems which contain additional constraints in the form of directed graphs whose vertex set corresponds to the item set. In the one-neighbor knapsack problem, an item can be chosen only if at least one of its neighbors is chosen. In the all-neighbors knapsack problem, an item can be chosen only if all its neighbors are chosen. For both problems, we consider uniform and general profits and weights. We prove upper bounds for the time complexity of these problems when restricting the graph constraints to special sets of digraphs. We discuss directed co-graphs, minimal series-parallel digraphs, and directed trees.

Best Arm Identification in Spectral Bandits

We study best-arm identification with fixed confidence in bandit models with graph smoothness constraint. We provide and analyze an efficient gradient ascent algorithm to compute the sample complexity of this problem as a solution of a non-smooth max-min problem (providing in passing a simplified analysis for the unconstrained case). Building on this algorithm, we propose an asymptotically optimal strategy. We furthermore illustrate by numerical experiments both the strategy's efficiency and the impact of the smoothness constraint on the sample complexity. Best Arm Identification (BAI) is an important challenge in many applications ranging from parameter tuning to clinical trials. It is now very well understood in vanilla bandit models, but real-world problems typically involve some dependency between arms that requires more involved models. Assuming a graph structure on the arms is an elegant practical way to encompass this phenomenon, but this had been done so far only for regret minimization. Addressing BAI with graph constraints involves delicate optimization problems for which the present paper offers a solution.

Diversity of graph models and graph generators in mutation testing

When custom modeling tools are used for designing complex safety-critical systems (e.g., critical cyber-physical systems), the tools themselves need to be validated by systematic testing to prevent tool-specific bugs reaching the system. Testing of such modeling tools relies upon an automatically generated set of models as a test suite. While many software testing practices recommend that this test suite should be diverse, model diversity has not been studied systematically for graph models. In the paper, we propose different diversity metrics for models by generalizing and exploiting neighborhood and predicate shapes as abstraction. We evaluate such shape-based diversity metrics using various distance functions in the context of mutation testing of graph constraints and access policies for two separate industrial DSLs. Furthermore, we evaluate the quality (i.e., bug detection capability) of different (random and consistent) model generation techniques for mutation testing purposes.