Margarida Carvalho

A complexity and approximability study of the bilevel knapsack problem

We analyze three fundamental variants of the bilevel knapsack problem, which all are complete for the second level of the polynomial hierarchy. If the weight and profit coefficients in the knapsack problem are encoded in unary, then two of the bilevel variants are solvable in polynomial time, whereas the third is NP-complete. Furthermore we design a polynomial time approximation scheme for this third variant, whereas the other two variants cannot be approximated in polynomial time within any constant factor (assuming P≠NP).

A study on the computational complexity of the bilevel knapsack problem

We analyze the computational complexity of three fundamental variants of the bilevel knapsack problem. All three variants are shown to be complete for the second level of the polynomial hierarchy. We also discuss the somewhat easier situation where the weight and profit coefficients in the knapsack problem are encoded in unary: two of the considered bilevel variants become solvable in polynomial time, whereas the third becomes NP-complete. Furthermore, we design a polynomial time approximation scheme for this third variant, whereas the other two variants cannot be approximated in polynomial time within any constant factor (assuming P\;

Bilevel Knapsack with Interdiction Constraints

\ne

Validation of otolith daily increments in early juveniles of shanny Lipophrys pholis.

\;NP).

Pelagic larval duration, size at settlement and coastal recruitment of the intertidal blenny Lipophrys pholis

We consider a bilevel integer programming model that extends the classic 0–1 knapsack problem in a very natural way. The model describes a Stackelberg game where the leader’s decision interdicts a subset of the knapsack items for the follower. As this interdiction of items substantially increases the difficulty of the problem, it prevents the application of the classical methods for bilevel programming and of the specialized approaches that are tailored to other bilevel knapsack variants. Motivated by the simple description of the model, by its complexity, by its economic applications, and by the lack of algorithms to solve it, we design a novel viable way for computing optimal solutions. Finally, we present extensive computational results that show the effectiveness of the new algorithm on instances from the literature and on randomly generated instances.

Ontogenetic development of the sagittal otoliths of Lipophrys pholis (Blenniidae) during the embryonic, larval and settlement stages

To assess the periodicity of micro-increment formation in otoliths of Lipophrys pholis, 90 early juveniles were immersed in alizarin red S or tetracycline hydrochloride for 24 h and sacrificed after 10, 20 and 30 days. The number of micro-increments viewed under light microscopy was significantly related to the duration of the experimental period, and the slopes of the linear regressions were not significantly different from 1. This study indicates that micro-increments in sagittae were deposited daily and can be used as reliable sources of age information for L. pholis.

Nash equilibria in the two-player kidney exchange game

To study some early life history traits of Lipophrys pholis , 110 recruits (TL ≤ 30 mm) were collected in April and May 2013 during the low tide periods in four rocky beaches along the west (Cabo do Mundo, Peniche and Vale do Homem) and south (Olhos de Agua) Portuguese coasts. Pelagic larval duration, size at settlement and age at coastal recruitment were back-calculated from the microstructure of otoliths. Pelagic larval duration estimated from micro-increment counts until the settlement marks ranged from 57 to 73 days and showed a latitudinal reduction trend from north to south. This variable seems to be related in 30% with the regional seawater temperatures probably through the direct effect on the somatic growth. Settlement sizes (~19 mm) did not show any regional differences suggesting that this is a more conservative character within species. The mean age at coastal recruitment varied between 69 and 93 days, but northern individuals were recruited at an older age. Back-calculated spawning, hatching and settlement dates appear to be unrelated to the lunar cycle for L. pholis .

Movement, connectivity and population structure of the intertidal fish Lipophrys pholis as revealed by otolith oxygen and carbon stable

Eggs and settlers of Lipophrys pholis were collected during low tides from a northern Portuguese rocky beach in March and May of 2013. The eggs were reared under controlled-laboratory conditions until the larval stage, while settlers were immediately sacrificed. Sagittae were viewed by scanning electron microscopy to assess the occurrence of different microstructural checks during embryonic, larval and settlement stages. Otoliths recorded several micro-increments (8–10) before hatching in late embryo phases. In larval otoliths a visible hatching check was observed and micro-increments were deposited on a daily basis. Early settlers presented in the otolith edge two types of settlement marks. These findings are important to prevent a misidentification of some life history events and/or to avoid overestimation of individual age from otolith studies.

A polynomial algorithm for a continuous bilevel knapsack problem

Kidney exchange programs have been set in several countries within national, regional or hospital frameworks, to increase the possibility of kidney patients being transplanted. For the case of hospital programs, it has been claimed that hospitals would benefit if they collaborated with each other, sharing their internal pools and allowing transplants involving patients of different hospitals. This claim led to the study of multi-hospital exchange markets. We propose a novel direction in this setting by modeling the exchange market as an integer programming game. The analysis of the strategic behavior of the entities participating in the kidney exchange game allowed us to prove that the most rational game outcome maximizes the social welfare and that it can be computed in polynomial time.

Existence of Nash Equilibria on Integer Programming Games

ABSTRACT The shanny Lipophrys pholis is an intertidal fish commonly found in Portuguese coastal waters. Spawning takes place from early autumn to mid spring, after which demersal eggs hatch and larvae disperse along the coast. Two to three months later, young juveniles return to the tide pools to settle. However, information on fish movement, habitat connectivity and population structure is scarce for this species. One hundred and twenty early juveniles (16–35 mm) were collected in April 2014 from six rocky beaches along the western and south Portuguese coasts (Agudela, Cabo do Mundo, Boa Nova, Peniche, Sines and Olhos de Água). δ18O and δ13C were determined by isotope-ratio mass spectrometry. Data were analysed to determine whether isotopic signatures could be used to assess the degree of separation between individuals collected from different locations. Mean δ13C and δ18O values ranged from −0.02‰ to 1.14‰ and −7.77‰ to −6.62‰, respectively. Both seawater temperature and salinity caused differences in otolith δ18O among the four main sampling areas. The variation among areas in δ13C was most likely related to slight differences in the diet, growth and metabolism of fish. The distinct isotopic signatures, at least for the northern and central areas, suggested low levels of connectivity across large spatial scales during the juvenile stage. Furthermore, similar isotopic signatures within the same area indicated some degree of larval oceanic retention at short spatial scales. This study suggests that stable isotope records in otoliths could provide information about the home residency, movements and habitat connectivity of intertidal fishes.