Let A be a set of n arcs on the unit circle. We present a new simple (n logn)-time algorithm for computing a minimum cut set for A (and a maximum independent subset of A). Our solution is based on a dynamic maintenance scheme for a set S of n intervals on the line, that enables us to update the current minimum cut set for S, following an insertion or a deletion of an interval, in time O(c logn)...

In this note, the cut C is referred as the cut-set and the size of the cut |C| as the size of the cut-set. For a graph, a maximum cut is a cut whose size is at least the size of any other cut. The problem of finding a maximum cut in a graph is known as the maximum cut problem. The problem is NP-hard. Simple 0.5approximation algorithms existed long time ago, but no improvement was made till 1990...

INTRODUCTION In a perspective of economic constraints the prioritizing of patients to IFN-free regimens is mainly based on the determination of liver stiffness by transient elastography (TE). Being a continuous variable the interpretation of TE results requires the identification of cut-off values, to date set to maximize diagnostic accuracy even if such values should be better based on more he...

Background: Some authors detected significantly higher IL-18 levels in serum, peritoneal, and pleural fluids of patients with severe OHSS as compared with control groups and suggest a role of IL- 18 as a marker of OHSS. Lower levels of IL-18 have been found to characterize unexplained infertility. In this study, we analyzed the importance of IL-18 levels in serum and follicle fluid in response ...

We introduce a problem we call Cooperative cut, where the goal is to find a minimum-cost graph cut but where a submodular function is used to define the cost of a subsets of edges. That means, the cost of an edge that is added to the current cut set C depends on the edges in C. This generalization of the cost in the standard min-cut problem to a submodular cost function immediately makes the pr...

We define a generalization CERES of the first-order cut-elimination method CERES to higher-order logic. At the core of CERES lies the computation of an (unsatisfiable) set of sequents CS(π) (the characteristic sequent set) from a proof π of a sequent S. A refutation of CS(π) in a higher-order resolution calculus can be used to transform cut-free parts of π (the proof projections) into a cut-fre...

We investigate the zero-forcing number for triangle-free graphs. We improve upon the trivial bound, δ ≤ Z(G) where δ is the minimum degree, in the triangle-free case. In particular, we show that 2δ− 2 ≤ Z(G) for graphs with girth of at least 5, and this can be further improved when G has a small cut set. Lastly, we make a conjecture that the lower bound for Z(G) increases as a function of the g...

Decision-theoretic rough set is a quite useful rough set by introducing the decision cost into probabilistic approximations of the target. However, Yao's decision-theoretic rough set is based on the classical indiscernibility relation; such a relation may be too strict in many applications. To solve this problem, a δ-cut decision-theoretic rough set is proposed, which is based on the δ-cut quan...

1. Max-3-SAT: In this case, Γ represents the OR-predicate. 2. Max-Cut: We can model this as a CSP where the vertices that get assigned to one side get 0 value and the other gets 1; so the domain set is D = {0, 1}. The set Γ contains only 6= predicate. 3. Max-E3-LIN2: The domain is {0, 1}. There are two types of precidates in Γ, i.e. xi + xj + xk = 0 and xi + xj = xk = 1 (under modolu two.) 4. M...

We describe a new circulation-based method to determine cuts in an undirected graph. A circulation is an oriented labeling of edges with integers so that at each vertex, the sum of the in-labels equals the sum of out-labels. For an integer k, our approach is based on simple algorithms for sampling a circulation (mod k) uniformly at random. We prove that with high probability, certain dependenci...