Structural Target Controllability of Linear Networks

Abstract

Computational analysis of the structure of intra-cellular molecular interaction networks can suggest novel therapeutic approaches for systemic diseases like cancer. Recent research in the area of network science has shown that network control theory can be a powerful tool in the understanding and manipulation of such bio-medical networks. In 2011, Liu et al. developed a polynomial time algorithm computing the size of the minimal set of nodes controlling a linear network. In 2014, Gao et al. generalized the problem for target control, minimizing the set of nodes controlling a target within a linear network. The authors developed a Greedy approximation algorithm while leaving open the complexity of the optimization problem. We prove here that the target controllability problem is NP-hard in all practical setups, i.e., when the control power of any individual input is bounded by some constant. We also show that the algorithm provided by Gao et al. fails to provide a valid solution in some special cases, and an additional validation step is required. We fix and improve their algorithm using several heuristics, obtaining in the end an up to 10-fold decrease in running time and also a decrease in the size of solutions.

Functional Target Controllability of Networks: Structural Properties and Efficient Algorithms

“…The second difficulty is the intrinsic hardness of the problem: the Minimum Controllability Problem for target controllability has recently been proved to be a NP-hard problem [27]. This negative result implies the need for heuristic solutions in practical situations: one such approximate algorithm is provided in [27].…”

Target controllability of multiagent systems under fixed and switching topologies

“…Instead, it is more feasible and sufficient to achieve target control of MASs, that is, to control a subset of agents. This specific form of output controllability is known under the name target controllability . In the recent literature, the target controllability has been intensively studied by many researchers.…”

“…To the best of our knowledge, however, the existing results considered target controllability under structural (strongly structurally) controllability framework. Thus, the results inevitably ignored the effects of link weights on target controllability . On the other hand, the existing results of target controllability are only pertinent to the fixed interaction topology while switching topology is left largely unconsidered …”

“…[34][35][36][37][38] In the recent literature, the target controllability has been intensively studied by many researchers. Examples include the target controllability of complex networks, 34,35 strong target controllability of dynamical networks, 36,37 structural target controllability of undirected networks, 38 and target controllability of biomolecular networks. 39 To the best of our knowledge, however, the existing results considered target controllability under structural (strongly structurally) controllability framework.…”

“…34,35,[37][38][39] On the other hand, the existing results of target controllability are only pertinent to the fixed interaction topology while switching topology is left largely unconsidered. [34][35][36][37][38][39] In this paper, we study the target controllability of MASs under fixed and switching topologies. For fixed interaction topology, we provide some necessary and/or sufficient algebraic and graph-theoretic conditions for target controllability and analyze the effects of the directed and weighted interaction topology on target controllability.…”