Tropical deforestation for agriculture causes alarming CO2 emissions and loss of biodiversity and ecosystem services. To prevent this, various governments and multinational commodity-buyers offer a positive incentive for locals conditional on no deforestation in a specified area. As an alternative to the area no-deforestation condition, we propose a weaker "regeneration condition": if forest is cleared on land in the specified area, locals prevent its economic use, enabling the forest to regenerate. With innovation in cooperative game theory, we characterize the best condition (area no-deforestation vs. area regeneration) and feasible incentives to prevent deforestation and to compensate each local for his missed economic opportunity. The regeneration condition is best in an area with the potential for entrants to engage in deforestation. Without entrants, if locals can cooperate, the area no-deforestation condition is best, and works with any incentive that is more valuable for locals collectively than deforestation. By surveying smallholder palm farmers in 58 villages of East Kalimantan, Indonesia, we fit our model with a price premium for palm fruit as the incentive, in each village as the area. A price premium is an imperfect incentive, having least value for a farmer with the least land and, correspondingly, high temptation to engage in deforestation. The Roundtable on Sustainable Palm Oil (RSPO) price premium is too low. Still, with a moderate price premium, our area regeneration condition prevents deforestation in most villages and is remarkably robust to deter potential entrants.

Many operational settings share the following three features: (i) a centralized planning system allocates tasks to workers or service providers, (ii) the providers generate value by completing the tasks, and (iii) the completion of tasks influences the providers’ welfare. In such cases, the planning system’s allocations often entail trade-offs between the service providers’ welfare and the total value that is generated (or that accrues to the system itself), and concern arises that allocations that are good under one metric may perform poorly under the other. We propose a broad framework for quantifying the magnitude of value losses when allocations are restricted to satisfy certain desirable guarantees to the service providers. We consider a general class of guarantees that includes many considerations of practical interest arising (e.g., in the design of sustainable two-sided markets) in workforce welfare and compensation, or in sourcing and payments in supply chains, among other application domains. We derive tight bounds on the relative value loss and show that this loss is limited for any restriction included in our general class. Our analysis shows that when many providers are present, the largest losses are driven by fairness considerations, whereas when few providers are present, they are driven by the heterogeneity in the providers’ effectiveness to generate value; when providers are perfectly homogenous, the losses never exceed 50%. We study additional loss drivers and find that less variability in the value of jobs and a more balanced supply-demand ratio may lead to larger losses. Lastly, we demonstrate numerically using both real-world and synthetic data that the loss can be small in several cases of practical interest. This paper was accepted by Chung Piaw Teo, optimization.

To respond to pandemics such as COVID-19, policy makers have relied on interventions that target specific population groups or activities. Because targeting is operationally challenging and contentious, rigorously quantifying its benefits and designing practically implementable policies that achieve some of these benefits is critical for effective and equitable pandemic control. We propose a flexible framework that leverages publicly available data and a novel optimization algorithm based on model predictive control and trust region methods to compute optimized interventions that can target two dimensions of heterogeneity: age groups and the specific activities that individuals normally engage in. We showcase a complete implementation focused on the Île-de-France region of France and use this case study to quantify the benefits of dual targeting and to propose practically implementable policies. We find that dual targeting can lead to Pareto improvements, reducing the number of deaths and the economic losses. Additionally, dual targeting allows maintaining higher activity levels for most age groups and, importantly, for those groups that are most confined, thus leading to confinements that are arguably more equitable. We then fit decision trees to explain the decisions and gains of dual-targeted policies and find that they prioritize confinements intuitively, by allowing increased activity levels for group-activity pairs with high marginal economic value prorated by social contacts, which generates important complementarities. Because dual targeting can face significant implementation challenges, we introduce two practical proposals inspired by real-world interventions — based on curfews and recommendations — that achieve a significant portion of the benefits without explicitly discriminating based on age.

Given a simple graph G, a set \(C \subseteq V(G)\) is a neighborhood cover set if every edge and vertex of G belongs to some G[v] with \(v \in C\), where G[v] denotes the subgraph of G induced by the closed neighborhood of the vertex v. Two elements of \(E(G) \cup V(G)\) are neighborhood-independent if there is no vertex \(v\in V(G)\) such that both elements are in G[v]. A set \(S\subseteq V(G)\cup E(G)\) is neighborhood-independent if every pair of elements of S is neighborhood-independent. Let \(\rho _{\mathrm {n}}(G)\) be the size of a minimum neighborhood cover set and \(\alpha _{\mathrm {n}}(G)\) of a maximum neighborhood-independent set. Lehel and Tuza defined neighborhood-perfect graphs G as those where the equality \(\rho _{\mathrm {n}}(G^\prime ) = \alpha _{\mathrm {n}}(G^\prime )\) holds for every induced subgraph \(G^\prime \) of G. In this work we prove forbidden induced subgraph characterizations of the class of neighborhood-perfect graphs, restricted to two superclasses of cographs: \(P_4\)-tidy graphs and tree-cographs. We give as well linear-time algorithms for solving the recognition problem of neighborhood-perfect graphs and the problem of finding a minimum neighborhood cover set and a maximum neighborhood-independent set in these same classes. Finally we prove that although for complements of trees finding these optimal sets can be achieved in linear-time, for complements of bipartite graphs it is \(\mathrm {NP}\)-hard.

We model a communication system by a network, were the terminals are perfect but links may fail randomly, with identical probability q = 1 - p. This defines a partial random network. The all-terminal reliability R(p) is the probability that this random graph is connected, and it is a polynomial in p. Finding the reliability polynomial can be reduced to a hard counting problem.The contributions of this paper are two-fold. First, we fully determine all subgraphs that accept an easy counting technique, and as a consequence, the reliability polynomial is directly retrieved. More specifically, we define the "level of difficulty" of a graph, and find the reliability polynomials of all graphs with non-positive level of difficulty.The second contribution is to propose a fundamental problem from survivable network design, called the Network Utility Problem. The goal is to maximize the network utility, under a minimum edge-connectivity requirement. The network utility is defined as the opposite of the level of difficulty minus one, and it is never greater than unity. The upper-bound is achieved only in trees and cycles. We prove that Harary graphs achieve the optimal value for the Network Utility Problem. Finally, we present open problems that provide hints for future work.

Given a simple graph G, a set C ⊆ V(G) is a neighborhood cover set if every edge and vertex of G belongs to some G[v] with v ∈ C, where G[v] denotes the subgraph of G induced by the closed neighborhood of the vertex v. Two elements of E(G) ∪ V(G) are neighborhood-independent if there is no vertex v∈ V(G) such that both elements are in G[v]. A set S⊆ V(G)∪ E(G) is neighborhood-independent if every pair of elements of S is neighborhood-independent. Let ρ_n(G) be the size of a minimum neighborhood cover set and α_n(G) of a maximum neighborhood-independent set. Lehel and Tuza defined neighborhood-perfect graphs G as those where the equality ρ_n(G') = α_n(G') holds for every induced subgraph G' of G. In this work we prove forbidden induced subgraph characterizations of the class of neighborhood-perfect graphs, restricted to two superclasses of cographs: P_4-tidy graphs and tree-cographs. We give as well linear-time algorithms for solving the recognition problem of neighborhood-perfect graphs and the problem of finding a minimum neighborhood cover set and a maximum neighborhood-independent set in these same classes.