Integrality Gap Research Articles

Cover by disjoint cliques cuts for the knapsack problem with conflicting items

The knapsack problem with conflicting items arises in several real-world applications. We propose a family of strong cutting planes and prove that a subfamily of these cuts can be facet-defining. Computational experiments show that the proposed cuts are very effective in reducing integrality gaps, providing dual bounds up to 78% tighter than formulations strengthened with traditional combinatorial cuts. We also show that it is possible to adapt a recently proposed lifting procedure to further strengthen the proposed cuts.

On the Weisfeiler-Leman dimension of fractional packing

The k-dimensional Weisfeiler-Leman procedure (k-WL), which colors k-tuples of vertices in rounds based on the neighborhood structure in the graph, has proven to be immensely fruitful in the algorithmic study of Graph Isomorphism. More generally, it is of fundamental importance in understanding and exploiting symmetries in graphs in various settings. Two graphs are k-WL-equivalent if the k-dimensional Weisfeiler-Leman procedure produces the same final coloring on both graphs. 1-WL-equivalence is known as fractional isomorphism of graphs, and the k-WL-equivalence relation becomes finer as k increases.We investigate to what extent standard graph parameters are preserved by k-WL-equivalence, focusing on fractional graph packing numbers. The integral packing numbers are typically NP-hard to compute, and we discuss applicability of k-WL-invariance for estimating the integrality gap of the LP relaxation provided by their fractional counterparts.

Optimal Agent Framework: A Novel, Cost-Effective Model Articulation to Fill the Integration Gap between Agent-Based Modeling and Decision-Making

Making proper decisions in today’s complex world is a challenging task for decision makers. A promising approach that can support decision makers to have a better understanding of complex systems is agent-based modeling (ABM). ABM has been developing during the last few decades as a methodology with many different applications and has enabled a better description of the dynamics of complex systems. However, the prescriptive facet of these applications is rarely portrayed. Adding a prescriptive decision-making (DM) aspect to ABM can support the decision makers in making better or, in some cases, optimized decisions for the complex problems as well as explaining the investigated phenomena. In this paper, first, the literature of DM with ABM is inquired and classified based on the methods of integration. Performing a scientometric analysis on the relevant literature lets us conclude that the number of publications attempting to integrate DM and ABM has not grown during the last two decades, while analysis of the current methodologies for integrating DM and ABM indicates that they have serious drawbacks. In this regard, a novel nature-inspired model articulation called optimal agent framework (OAF) has been proposed to ameliorate the disadvantages and enhance the realization of proper decisions in ABM at a relatively low computational cost. The framework is examined with the Bass diffusion model. The results of the simulation for the customized model developed by OAF have verified the feasibility of the framework. Moreover, sensitivity analyses on different agent populations, network structures, and marketing strategies have depicted the great potential of OAF to find the optimal strategies in various stochastic and unconventional conditions which have not been addressed prior to the implementation of the framework.

Bacterial translocation and microgap formation at a novel conical indexed implant abutment system for single crowns

ObjectivesA conometric concept was recently introduced in which conical implant abutments hold the matching crown copings by friction alone, eliminating the need for cement or screws. The aim of this in vitro study was to assess the presence of microgap formation and bacterial leakage at the Acuris conometric restorative interface of three different implant abutment systems.Material and methodsA total of 75 Acuris samples of three implant-abutment systems (Ankylos, Astra Tech EV, Xive) were subjected to microbiological (n = 60) and scanning electron microscopic (SEM) investigation (n = 15). Bacterial migration into and out of the conical coupling system were analyzed in an anaerobic workstation for 48, 96, 144, and 192 h. Bacterial DNA quantification using qrt-PCR was performed at each time point. The precision of the conometric coupling and internal fit of cemented CAD/CAM crowns on corresponding Acuris TiN copings were determined by means of SEM.Resultsqrt-PCR results failed to demonstrate microbial leakage from or into the Acuris system. SEM analysis revealed minute punctate microgaps at the apical aspect of the conometric junction (2.04 to 2.64 µm), while mean cement gaps of 12 to 145 µm were observed at the crown-coping interface.ConclusionsThe prosthetic morse taper connection of all systems examined does not allow bacterial passage. Marginal integrity and internal luting gap between the ceramic crown and the coping remained within the clinically acceptable limits.Clinical relevanceConometrically seated single crowns provide sufficient sealing efficiency, relocating potential misfits from the crown-abutment interface to the crown-coping interface.

Efficient constructions of convex combinations for 2-edge-connected subgraphs on fundamental classes

We present coloring-based algorithms for tree augmentation and use them to construct convex combinations of 2-edge-connected subgraphs. This classic tool has been applied previously to the problem, but our algorithms illustrate its flexibility, which – in coordination with the choice of spanning tree – can be used to obtain various properties (e.g., 2-vertex connectivity) that are useful in our applications.We use these coloring algorithms to design approximation algorithms for the 2-edge-connected multigraph problem (2ECM) and the 2-edge-connected spanning subgraph problem (2ECS) on two well-studied types of LP solutions. The first type of points, half-integer square points, belong to a class of fundamental extreme points, which exhibit the same integrality gap as the general case. For half-integer square points, the integrality gap for 2ECM is known to be between 65 and 43. We improve the upper bound to 97. The second type of points we study are uniform points whose support is a 3-edge-connected graph and each entry is 23. Although the best-known upper bound on the integrality gap of 2ECS for these points is less than 43, previous results do not yield an efficient algorithm. We give the first approximation algorithm for 2ECS with ratio below 43 for this class of points.

Book Review: Shrinking the Integrity Gap: Between What Leaders Preach and Live by Jeff Mattson and Terra A. Mattson

Book Review: <i>Shrinking the Integrity Gap: Between What Leaders Preach and Live</i> by Jeff Mattson and Terra A. Mattson

Book review: Glenn D Walters, Closing the Integration Gap in Criminology. The Case for Criminological Thinking

Book review: Glenn D Walters, <i>Closing the Integration Gap in Criminology. The Case for Criminological Thinking</i>

Fair colorful k-center clustering

An instance of colorfulk-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius rho such that there exist balls of radius rho around k of the points that meet the coverage requirements. The motivation behind this problem is twofold. First, from fairness considerations: each color/group should receive a similar service guarantee, and second, from the algorithmic challenges it poses: this problem combines the difficulties of clustering along with the subset-sum problem. In particular, we show that this combination results in strong integrality gap lower bounds for several natural linear programming relaxations. Our main result is an efficient approximation algorithm that overcomes these difficulties to achieve an approximation guarantee of 3, nearly matching the tight approximation guarantee of 2 for the classical k-center problem which this problem generalizes. algorithms either opened more than k centers or only worked in the special case when the input points are in the plane.

A systematic mapping protocol for understanding knowledge exchange in forest science

Abstract When making decisions about forest and environmental management, managers and policymakers often rely upon scientific knowledge. There is a well‐documented ‘knowledge–integration gap’ where often the production of knowledge and its use are not aligned. Though there are several theoretical frameworks that conceptualize how knowledge is exchanged between producers of scientific knowledge and users of that information, there has been little attention to documenting knowledge exchange practices and their effectiveness, especially about forests. In the systematic map, we will examine the peer‐reviewed academic and grey literature to document and classify the knowledge exchange techniques suggested and adopted by knowledge producers and users in the forest sciences globally. Characterizing this knowledge exchange landscape will provide new information about which techniques are used and their frequency, if there is evidence of effectiveness for particular techniques, and recommendations for best practices. This map will also show whether approaches to knowledge exchange differ between sectors (e.g. academia, government). We will create a systematic literature map as defined by the Collaboration for Environmental Evidence to capture case studies of, or theories about, knowledge exchange related to forest science. The search of peer‐reviewed academic and grey literature will be conducted in English and French in two academic databases (BASE and Scopus) and one specialist database (ResearchGate). Candidate search strings will be evaluated against a test list of documents to determine strings with maximum sensitivity and specificity. Eligibility criteria will be applied to items at two screening stages: (1) title and abstract and (2) full‐text. All screening decisions will be recorded in a database with 15% of full‐text screening decisions validated. Items retained for inclusion will have data extracted according to a standardized strategy. Each reviewer conducting data extraction will have at least three of their extractions validated. The systematic map will employ a narrative synthesis approach that includes descriptive statistics, tables, and figures which describe the types and frequency of knowledge exchange techniques theorized or described, a network map displaying the institutions within and between which knowledge exchange occurs, as well as summarizing any available evidence of effectiveness for particular knowledge exchange techniques.

Matchings under distance constraints I.

This paper introduces the d-distance matching problem, in which we are given a bipartite graph G=(S,T;E) with S={s_1,dots ,s_n}, a weight function on the edges and an integer din mathbb Z_+. The goal is to find a maximum-weight subset Msubseteq E of the edges satisfying the following two conditions: (i) the degree of every node of S is at most one in M, (ii) if s_it,s_jtin M, then |j-i|ge d. This question arises naturally, for example, in various scheduling problems. We show that the problem is NP-complete in general and admits a simple 3-approximation. We give an FPT algorithm parameterized by d and also show that the case when the size of T is constant can be solved in polynomial time. From an approximability point of view, we show that the integrality gap of the natural integer programming model is at most 2-frac{1}{2d-1}, and give an LP-based approximation algorithm for the weighted case with the same guarantee. A combinatorial (2-frac{1}{d})-approximation algorithm is also presented. Several greedy approaches are considered, and a local search algorithm is described that achieves an approximation ratio of 3/2+epsilon for any constant epsilon >0 in the unweighted case. The novel approaches used in the analysis of the integrality gap and the approximation ratio of locally optimal solutions might be of independent combinatorial interest.

Even worse than the undocumented? Assessing the refugees’ integration in the labour market of Lombardy (Italy) in 2001–2014

AbstractThe paper aimed to assess possible gaps in labour market integration or refugees compared with other migrants, including irregular migrants in the Italian region of Lombardy in 2001–2014. Despite the Italian labour market's remarkable capacity to integrate foreign workers, our findings support the results of studies carried out in other contexts on a ‘refugee gap’ in labour market integration. Our research shows that refugees have more considerable difficulties integrating into the labour market than other migrants and notably compared with their co‐nationals, including those undocumented that may be in refugee‐like situations. Refugees show higher unemployment levels, irregular employment and a higher incidence of very low monthly work‐related incomes compared with other regular migrants. At the same time, they show higher levels of unemployment compared with irregular migrants.

Benefit of China's Social Health Insurance Schemes: Trend Analysis and Associated Factors Since Health Reform.

With the deepening of health insurance reform in China, the integration of social health insurance schemes was put on the agenda. This paper aims to illustrate the achievements and the gaps in integration by demonstrating the trends in benefits available from the three social health insurance schemes, as well as the influencing factors. Data were drawn from the three waves of the China Health and Nutrition Survey (2009, 2011, 2015) undertaken since health reforms commenced. χ2, Kruskal–Wallis test, and the Two-Part model were employed in the analysis. The overall reimbursement rate of the Urban Employee Basic Medical Insurance (UEBMI) is higher than that of Urban Resident Basic Medical Insurance (URBMI) or the New Rural Cooperative Medical Scheme (NRCMS) (p < 0.001), but the gap has narrowed since health reform began in 2009. Both the outpatient and inpatient reimbursement amounts have increased through the URBMI and NRCMS. Illness severity, higher institutional level, and inpatient service were associated with significant increases in the amount of reimbursement received across the three survey waves. The health reform improved benefits covered by the URBMI and NRCMS, but gaps with the UEBMI still exist. The government should consider more the release of health benefits and how to lead toward healthcare equity.

The complexity of stakeholder influence on MaaS: A study on multi-stakeholder perspectives in Shenzhen self-driving mini-bus case

Emerging technologies are changing our preferences for transportation solutions, which focus on service efficiency, safety, and sustainability. Mobility as a service (MaaS) is a user-oriented transportation solution that integrates both public and private operators into the same platform. The implementation of MaaS aims to simplify users’ booking procedures and increase the usability of various kinds of transportation resources. However, the integration of a myriad of transportation subsystems raises interpretation challenges from associated multi-stakeholder and subsystems. To overcome these challenges, the authors have involved different stakeholders from related subsystems to reveal concerns. This study aims to analyse a novel public transportation system - the self-driving mini-bus service in Shenzhen. The result shows that system characteristics and stakeholder concerns can be established using an Action, Factor and Goal structure. Stakeholders involved described their perceptions of self-driving bus integration in MaaS. The description could be used by analysts to uncover integration gaps further and could be updated by involving more stakeholders according to project developments. This study highlights the complexity of self-driving mini-buses integration challenges in MaaS from a stakeholder perspective, which provides learnings to advance the MaaS adoption in the future.

Addressing gaps in adolescent tuberculosis programming and policy in Nigeria from a public health perspective

Tuberculosis (TB) is a leading infectious cause of death globally. Of the estimated 10 million people who developed active TB in 2019, 1.8 million (18%) were adolescents and young adults aged 15-24 years. Adolescents have poorer rates of TB screening, treatment initiation and completion compared to adults. Unfortunately, there is relatively less programme, research and policy focus on TB for adolescents aged 10-19 years. This article reviews the scope of health services and the relevant policy landscape for TB case notification and care/treatment, TB/HIV management, and latent TB infection for adolescents in Nigeria. Additionally, it discusses considerations for TB vaccines in this population. All Nigeria Federal Ministry of Health policy documents relevant to adolescent health services and TB, and published between 2000 and 2020 underwent narrative review. Findings were reported according to the service areas outlined in the Objectives. Nine policy documents were identified and reviewed. While multiple policies acknowledge the needs of adolescents in public health and specifically in TB programming, these needs are often not addressed in policy, nor in program integration and implementation. The lack of age-specific epidemiologic and clinical outcomes data for adolescents contributes to these policy gaps. Poor outcomes are driven by factors such as HIV co-infection, lack of youth-friendly health services, and stigma and discrimination. Policy guidelines and innovations should include adaptations tailored to adolescent needs. However, these adaptations cannot be developed without robust epidemiological data on adolescents at risk of, and living with TB. Gaps in TB care integration into primary reproductive, maternal-child health and nutrition services should be addressed across multiple policies, and mechanisms for supervision, and monitoring and evaluation of integration be developed to guide comprehensive implementation. Youth-friendly TB services are recommended to improve access to quality care delivered in a patient-centered approach.

Semidefinite Programming Relaxations of the Traveling Salesman Problem and Their Integrality Gaps

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, for example, algebraic connectivity, permutation matrices, and association schemes. The main results of this paper are twofold. First, de Klerk and Sotirov [de Klerk E, Sotirov R (2012) Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry. Math. Programming 133(1):75–91.] present a semidefinite program (SDP) based on permutation matrices and symmetry reduction; they show that it is incomparable to the subtour elimination linear program but generally dominates it on small instances. We provide a family of simplicial TSP instances that shows that the integrality gap of this SDP is unbounded. Second, we show that these simplicial TSP instances imply the unbounded integrality gap of every SDP relaxation of the TSP mentioned in the survey on SDP relaxations of the TSP in section 2 of Sotirov [Sotirov R (2012) SDP relaxations for some combinatorial optimization problems. Anjos MF, Lasserre JB, eds., Handbook on Semidefinite, Conic and Polynomial Optimization (Springer, New York), 795–819.]. In contrast, the subtour linear program performs perfectly on simplicial instances. The simplicial instances thus form a natural litmus test for future SDP relaxations of the TSP.

Linear Program-Based Approximation for Personalized Reserve Prices

We study the problem of computing data-driven personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a data set that contains the submitted bids of n buyers in a set of auctions, and the problem is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r. For this problem, which is known to be NP complete, we present a novel linear program (LP) formulation and a rounding procedure, which achieves a 0.684 approximation. This improves over the [Formula: see text]-approximation algorithm from Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which shows that it is impossible to design an algorithm that yields an approximation factor larger than 0.828 with respect to this LP. This paper was accepted by Chung Piaw Teo, Management Science Special Section on Data-Driven Prescriptive Analytics.

A search for a fifth planet around HR 8799 using the star-hopping RDI technique at VLT/SPHERE

Context.Direct imaging of extrasolar giant planets demands the highest possible contrasts (ΔH ≳ 10 mag) at the smallest angular separations (∼0.1″) from the star. We present an adaptive optics observing method, called star-hopping, recently offered as standard queue observing (service mode) for the SPHERE instrument at the VLT. The method uses reference difference imaging (RDI) but, unlike earlier RDI applications, images of a reference star for PSF subtraction are obtained within minutes of observing the target star.Aims.We aim to significantly gain in contrast beyond the conventional angular differencing imaging (ADI) method to search for a fifth planet at separations less than 10 au, interior to the four giant planets of the HR 8799 system. The most likely semimajor axes allowed for this hypothetical planet, which were estimated via dynamical simulations in earlier works, were 7.5 au and 9.7 au within a mass range of 1–8MJup.Methods.We obtained 4.5 h of simultaneous low-resolution integral field spectroscopy (R ∼ 30,Y − Hband with IFS) and dual-band imaging (K1 andK2 bands with IRDIS) of the HR 8799 system, interspersed with observations of a reference star. The reference star was observed for about one-third of the total time and generally needs to be of similar brightness (ΔR ≲ 1 mag) and separated on sky by ≲1–2°. The hops between stars were made every 6–10 min, with only 1 min gaps in on-sky integration per hop.Results.We did not detect the hypothetical fifth planet at the most plausible separations, 7.5 and 9.7 au, down to mass limits of 3.6MJupand 2.8MJup, respectively, but attained an unprecedented contrast limit of 11.2 magnitudes at 0.1″. We detected all four planets with high signal-to-noise ratios. TheYJHspectra for planetsc,dwere detected with redderH-band spectral slopes than found in earlier studies. As noted in previous works, the planet spectra are matched very closely by some red field dwarfs. Finally, comparing the current locations of the planets to orbital solutions, we found that planetseandcare most consistent with coplanar and resonant orbits. We also demonstrated that with star-hopping RDI, the contrast improvement at 0.1″ separation can be up to 2 mag.Conclusions.Since ADI, meridian transit and the concomitant sky rotation are not needed, the time of observation can be chosen from within a window that is two to three times larger. In general, star-hopping can be used for stars fainter thanR = 4 magnitudes, since for these a reference star of suitable brightness and separation is usually available.

Intellectual Properties Integration

Intellectual properties (IPs) integration is becoming more challenging due to the increasing complexity of systems on chip as well as their components. Since no survey is available about this topic, this paper is written to help recently interested researchers in the field to have an idea about IP integration. This paper tries to put the light on IP integration challenges over time and how researchers and industrials have dealt with every challenge. On the other hand, the emergence of the standard IP-XACT for packaging, integrating, and reusing intellectual properties has enabled the development of many integration tools and the enhancement of the already existing ones. In this regard, different solutions are presented in this paper before and after the emergence of the standard enriched with a discussion of different proposed solutions including an attempt to define what is needed to be done else. At the end, the paper concludes by considering a promising tendency that hopefully will mitigate some of IP integration gaps.

An LP-rounding based algorithm for a capacitated uniform facility location problem with penalties

Facility location problem is a well established research area within Operations Research. Capacitated facility location problem is one of the most important variants, in which each facility has an upper bound on the demand, i.e., capacity. Moreover, the integrality gap of the natural linear program relaxation for the problem is infinite. Fortunately, the gap is finite when all opening costs for the facilities are the same. We consider a capacity facility location problem with penalties in which it is allowed some customers are not served by facilities and all opening costs are uniform. Based on LP-rounding framework, we propose a 5.732-approximation algorithm.

Chvátal Rank in Binary Polynomial Optimization

Recently, several classes of cutting planes have been introduced for binary polynomial optimization. In this paper, we present the first results connecting the combinatorial structure of these inequalities with their Chvátal rank. We determine the Chvátal rank of all known cutting planes and show that almost all of them have Chvátal rank 1. We observe that these inequalities have an associated hypergraph that is β-acyclic. Our second goal is to derive deeper cutting planes; to do so, we consider hypergraphs that admit β-cycles. We introduce a novel class of valid inequalities arising from odd β-cycles, that generally have Chvátal rank 2. These inequalities allow us to obtain the first characterization of the multilinear polytope for hypergraphs that contain β-cycles. Namely, we show that the multilinear polytope for cycle hypergraphs is given by the standard linearization inequalities, flower inequalities, and odd β-cycle inequalities. We also prove that odd β-cycle inequalities can be separated in linear time when the hypergraph is a cycle hypergraph. This shows that instances represented by cycle hypergraphs can be solved in polynomial time. Last, to test the strength of odd β-cycle inequalities, we perform numerical experiments that imply that they close a significant percentage of the integrality gap.