Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization

Solving the NP-hard Maximum Cut or Binary Quadratic Optimization Problem to optimality is important in many applications including Physics, Chemistry, Neuroscience, and Circuit Layout. The leading approaches based on linear/semidefinite programming require the separation of so-called odd-cycle inequalities for solving relaxations within their associated branch-and-cut frameworks. In their groundbreaking work, F. Barahona and A.R. Mahjoub have given an informal description of a polynomial-time separation procedure for the odd-cycle inequalities. Since then, the odd-cycle separation problem has broadly been considered solved. However, as we reveal, a straightforward implementation is likely to generate inequalities that are not facet-defining and have further undesired properties. Here, we present a more detailed analysis, along with enhancements to overcome the associated issues efficiently. In a corresponding experimental study, it turns out that these are worthwhile, and may speed up the solution process significantly

A Strategic Approach to Building Affordable Housing in Philadelphia

Calls on the city to coordinate affordable housing production subsidies with other public and private investments in order to build sustainable mixed-income neighborhoods with energy-efficient homes, ensuring economic growth and long-term affordability

Economic and social impact of introducing casino gambling: a review and assessment of the literature

Reviews and assesses the existing literature on the potential economic impact of introducing casino gambling into a community or region, first by discussing the casinos? effect on economic activity and growth within a community or region, and then by exploring their effect on government revenues. Also discusses the literature related to the economic impact of social costs widely associated with gambling, such as increases in crime, bankruptcy, and problem gambling.Gambling industry

How to spend $3.92 billion: stabilizing neighborhoods by addressing foreclosed and abandoned properties

The Housing and Economic Recovery Act of 2008 created the Neighborhood Stabilization Program (NSP), under which states, cities, and counties will receive a total of $3.92 billion to acquire, rehabilitate, demolish, and redevelop foreclosed and abandoned residential properties. These funds can stabilize hard-hit neighborhoods, putting them on the path to market recovery. This will only happen, however, if they are used in ways that are strategically targeted and sensitive to market conditions. This paper outlines 11 key principles that states, counties, and cities should follow as they plan for and use NSP funds.Housing and Economic Recovery Act; Neighborhood Stabilization Program (NSP); Foreclosure

Challenges of the small rental property sector

Most rental housing in America is found in small multifamily buildings and this sector provides most of the options for low- and moderate-income (LMI) renters. With a growing wave of investors buying distressed properties in LMI neighborhoods, there are concerns about the ability of investors to properly maintain their investments. The author explores the small multifamily sector and suggests ways that policymakers can move beyond code enforcement and provide a combination of carrots and sticks to incentivize and increase the presence of “good actors."Rental housing

Home ownership education and counseling: issues in research and definition

Many public- and private-sector initiatives support the expansion of home-ownership opportunities for low- and moderate-income households. This discussion paper assesses existing research on the effectiveness of home-ownership education and counseling and opportunities for future research. A limited number of printed copies are available.Home ownership

Improved Mixed-Integer Programming Models for Multiprocessor Scheduling with Communication Delays

We revise existing and introduce new mixed-integer programming models for the Multiprocessor Scheduling Problem with Communication Delays. At first, we show how to provably reduce the number of product variables necessary to explicitly linearize the so-called packing formulation that contains bilinear terms. Then, we reveal that the feasible region of almost all existing formulations contains redundant solutions and formulate new constraints in order to exclude these. At the same time, by exploiting further structural properties, the models are improved concerning their size, strength, and modeling complexity. The discussion of these improvements leads to new much more compact formulations which are then experimentally compared with each other and with other formulations from the literature. We set up a realistic scenario with a preprocessing of the task graphs, delivering the gained information equally to all the tested models and evaluate not only running times but also the obtained lower and upper bounds on the makespan objective for unsolved instances of a large scale benchmark set

Compact Linearization for Binary Quadratic Problems Comprising Linear Constraints

In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients and right hand sides. Quadratic constraints may exist in addition, and the technique may as well be applied if these impose the only nonlinearities, i.e., the objective function is linear. We present special cases of linear constraints (along with prominent combinatorial optimization problems where these occur) such that the associated compact linearization yields a linear programming relaxation that is provably as least as strong as the one obtained with a classical linearization method. Moreover, we show how to compute a compact linearization automatically which might be used, e.g., by general-purpose mixed-integer programming solvers

On separation pairs and split components of biconnected graphs

The decomposition of a biconnected graph G into its triconnected components is fundamental in graph theory and has a wide range of applications. Based on a palm tree of G, the algorithm by Hopcroft and Tarjan is able to compute them in linear time if some corrections are applied. Today, the algorithm is still considered very hard to understand and proofs of its correctness are technical and challenging. The article at hand provides a more comprehensive description of the algorithm, making it easier to understand and implement. Its correctness is validated by explicitly mapping the algorithmic detection criteria to the graph-theoretic characterization of type-1 and type-2 separation pairs. Further, it reveals further errors and inaccuracies in the common definitions. This includes the description and proofs of further properties and relationships of separation pairs. The presented results also answer the question whether and under which preconditions type-1 and type-2 pairs can be computed separately from each other