Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints

In this paper, we show $O(1.415^n)$-time and $O(1.190^n)$-space exact algorithms for 0-1 integer programs where constraints are linear equalities and coefficients are arbitrary real numbers. Our algorithms are quadratically faster than exhaustive search and almost quadratically faster than an algorithm for an inequality version of the problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work. Rather than improving the time and space complexity, we advance to a simple direction as inclusion of many NP-hard problems in terms of exact exponential algorithms. Specifically, we extend our algorithms to linear optimization problems

Corporate Debt Restructuring and Public Financial Institutions in Japan -Do Government-Affiliated Financial Institutions Soften Budget Constraints?

There are two different views on the effects of public financial institutions on corporate debt restructuring : the soft budget view and the hard budget view. The former view, which is held by Kornai (1979, 1983), Dewatripont and Maskin (1995), and others insists that because centralized public financial institutions have difficulty committing themselves to refrain from providing additional funds to distressed firms, corporate reorganizations often result in overinvestment. On the other hand, the latter view argues that public financial institutions should prefer corporate liquidation rather than the continuation of business because public financial institutions are secured by mortgages to a greater extent and are more reluctant to forgive the debts than private financial institutions. In this paper, I have empirically examined the role and impact of public financial institutions, government-affiliated financial institutions in particular, from the viewpoints of debtor-in-possession (DIP) financing and bankruptcy procedures for distressed firms. The conclusions of this paper are as follows. In the DIP financing, the Development Bank of Japan always takes the lead, followed by private financial institutions. Namely, so-called cowbell effect may exist, which is inconsistent with the hard budget view. Regarding the selection of bankruptcy procedures, firms that owed to government-affiliated financial institutions have a tendency to opt for private procedures which have the effect of delaying a drastic debt restructuring. This is consistent with the soft budget view.public financial institutions, bankruptcy procedures, debtor-in-possession financing

Consistent Digital Curved Rays and Pseudoline Arrangements

Representing a family of geometric objects in the digital world where each object is represented by a set of pixels is a basic problem in graphics and computational geometry. One important criterion is the consistency, where the intersection pattern of the objects should be consistent with axioms of the Euclidean geometry, e.g., the intersection of two lines should be a single connected component. Previously, the set of linear rays and segments has been considered. In this paper, we extended this theory to families of curved rays going through the origin. We further consider some psudoline arrangements obtained as unions of such families of rays

Correction of Blurring due to a Difference in Scanning Direction of Field-Free Line in Projection-Based Magnetic Particle Imaging

In projection-based magnetic particle imaging (MPI) with a field-free-line (FFL) encoding scheme, projection data are usually acquired by moving the FFL in a zigzag and a difference in the projection data occurs depending on the scanning direction of FFL, resulting in blurring in the reconstructed images. In this study, we developed a method for correcting the blur by deconvolution using a signal-delay constant ({\xi}). The {\xi} value for correction ({\xi}c) was determined by acquiring projection data in positive and negative directions and searching for the {\xi} value which minimized the 2-norm between the deconvolved projection data in the two directions. We validated our method using a line and A-shaped phantoms for various velocities of FFL (vFFL). The {\xi}c value correlated linearly with vFFL. The full width at half maximum of the line phantom decreased significantly after correction of the blur. The effectiveness of our method was also confirmed by the MPI images of the A-shaped phantom. These results suggest that our method will be useful for enhancing the reliability of projection-based MPI