In collective systems, the available agents are a limited resource that must be allocated among tasks to maximize collective performance. Computing the optimal allocation of several agents to numerous tasks through a brute-force approach can be infeasible, especially when each task’s performance scales differently with the increase of agents. For example, difficult tasks may require more agents to achieve similar performances compared to simpler tasks, but performance may saturate nonlinearly as the number of allocated agents increases. We propose a computationally efficient algorithm, based on marginal performance gains, for optimally allocating agents to tasks with concave scalability functions—including linear, saturating, and retrograde scaling—to achieve maximum collective performance. We test the algorithm by allocating a simulated robot swarm among collective decision-making tasks, where embodied agents sample their environment and exchange information to reach a consensus on spatially distributed environmental features. We vary task difficulties by different geometrical arrangements of environmental features in space (patchiness). In this scenario, decision performance in each task scales either as a saturating curve (following the Condorcet’s Jury Theorem (CJT) in an interference-free setup) or as a retrograde curve (when physical interference among robots restricts their movement). Using simple robot simulations, we show that our algorithm can be useful in allocating robots among tasks. Our approach aims to advance the deployment of future real-world multirobot systems.

In this paper, we study the problem of finding a periodic attractor of a Boolean network (BN), which arises in computational systems biology and is known to be NP-hard. Since a general case is quite hard to solve, we consider special but biologically important subclasses of BNs. For finding an attractor of period 2 of a BN consisting of n OR functions of positive literals, we present a polynomial time algorithm. For finding an attractor of period 2 of a BN consisting of n AND/OR functions of literals, we present an O(1:985(n)) time algorithm. For finding an attractor of a fixed period of a BN consisting of n nested canalyzing functions and having constant treewidth w, we present an O(n(2p(w+1))poly(n)) time algorithm.

An experimental study of the feasibility and accuracy of the acyclicity approach introduced in [14] for the inference of business relationships among autonomous systems (ASes) is provided. We investigate the maximum acyclic type-of-relationship problem: on a given set of AS paths, find a maximum-cardinality subset which allows an acyclic and valley-free orientation. Inapproximability and NP-hardness results for this problem are presented and a heuristic is designed. The heuristic is experimentally compared to most of the state-of-the-art algorithms on a reliable data set. It turns out that the proposed heuristic produces the least number of misclassified customer-to-provider relationships among the tested algorithms. Moreover, it is flexible in handling pre-knowledge in the sense that already a small amount of correct relationships is enough to produce a high-quality relationship classification. Furthermore, the reliable data set is used to validate the acyclicity assumptions. The findings demonstrate that acyclicity notions should be an integral part of models of AS relationships.

Given a p‐order A over a universe of strings (i.e., a transitive, reflexive, antisymmetric relation such that if $(x, y) \in A$, then $|x|$ is polynomially bounded by $|y|$), an interval size function of A returns, for each string x in the universe, the number of strings in the interval between strings $b(x)$ and $t(x)$ (with respect to A), where $b(x)$ and $t(x)$ are functions that are polynomial‐time computable in the length of x. By choosing sets of interval size functions based on feasibility requirements for their underlying p‐orders, we obtain new characterizations of complexity classes. We prove that the set of all interval size functions whose underlying p‐orders are polynomial‐time decidable is exactly #P. We show that the interval size functions for orders with polynomial‐time adjacency checks are closely related to the class FPSPACE(poly). Indeed, FPSPACE(poly) is exactly the class of all nonnegative functions that are an interval size function minus a polynomial‐time computable function. We study two important functions in relation to interval size functions. The function #DIV maps each natural number n to the number of nontrivial divisors of n. We show that #DIV is an interval size function of a polynomial‐time decidable partial p‐order with polynomial‐time adjacency checks. The function #MONSAT maps each monotone boolean formula F to the number of satisfying assignments of F. We show that #MONSAT is an interval size function of a polynomial‐time decidable total p‐order with polynomial‐time adjacency checks. Finally, we explore the related notion of cluster computation.