How to assign volunteers to tasks compatibly ? A graph theoretic and parameterized approach

In this paper we study a resource allocation problem that encodes correlation between items in terms of \conflict and maximizes the minimum utility of the agents under a conflict free allocation. Admittedly, the problem is computationally hard even under stringent restrictions because it encodes a variant of the {\sc Maximum Weight Independent Set} problem which is one of the canonical hard problems in both classical and parameterized complexity. Recently, this subject was explored by Chiarelli et al.~[Algorithmica'22] from the classical complexity perspective to draw the boundary between {\sf NP}-hardness and tractability for a constant number of agents. The problem was shown to be hard even for small constant number of agents and various other restrictions on the underlying graph. Notwithstanding this computational barrier, we notice that there are several parameters that are worth studying: number of agents, number of items, combinatorial structure that defines the conflict among the items, all of which could well be small under specific circumstancs. Our search rules out several parameters (even when taken together) and takes us towards a characterization of families of input instances that are amenable to polynomial time algorithms when the parameters are constant. In addition to this we give a superior 2^{m}|I|^{\Co{O}(1)} algorithm for our problem where $m$ denotes the number of items that significantly beats the exhaustive \Oh(m^{m}) algorithm by cleverly using ideas from FFT based fast polynomial multiplication; and we identify simple graph classes relevant to our problem's motivation that admit efficient algorithms

Resolute control: Forbidding candidates from winning an election is hard

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On the (Parameterized) Complexity of Almost Stable Marriage

In the Stable Marriage problem, when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the "no blocking pair" condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, the goal is to find a matching whose size exceeds that of a stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list. Unfortunately, the problem remains intractable even for the combined parameter k+t+d. Thus, we extend our study to the local search variant of this problem, in which we search for a matching that not only fulfills each of the above conditions but is "closest", in terms of its symmetric difference to the given stable matching, and obtain an FPT algorithm

Natural Products as Prominent Source of Bioactive Components with Anti-diabetic Potential

Type 2 diabetes (T2DM) is a chronic metabolic condition characterized by elevated blood sugar levels. It is caused by a combination of insulin resistance and insulin production impairment. The nuclear transcription factor peroxisome proliferator-activated receptor gamma (PPAR-gamma) is essential for glucose homeostasis and lipid metabolism. PPAR-g agonists are a family of medicines used to manage type 2 diabetes by improving blood sugar management and enhancing insulin sensitivity. For decades, natural materials have been utilized as traditional remedies, and many of them have been demonstrated to have anti-diabetic properties. Some natural compounds have been proven in recent investigations to activate PPAR-g. We employed molecular docking and physicochemical screening in this investigation to discover natural compounds with the potential to be developed as novel anti-diabetic medicines. A library of more than 50 natural compounds was tested against the PPAR-g ligand binding domain. We also assessed the ADMET and physicochemical features of the compounds found to determine that they are drug-like. Our study shows the Drug-likeness, bioactivity score along with good ADMEt profile of various phytoconstituents with their high binding affinity toward PPAR-g (PDB ID: 2XKW) as a major target for T2DM. Physicochemical properties of selected compounds were done with SWISS ADME server while ADMEt screening was done by pkCSM server. The binding affinity and molecular interaction study of natural compounds with PPAR-g was done by using Molegro Virtual Docker (MVD). The MolDock and Rerank score of the top one compound of each category was taken to check the binding interaction with tubulin