BACKGROUND The optimal iliac screw path was determined to provide references for lumbosacral-pelvic reconstruction. METHODS Radiographic data of 100 patients with normal pelvis were selected for this study. Four paths were designed. Paths A, B, and C were from the starting point of the crossing point of the chiotic line and posterior iliac crest (CLIC, located at 24.0 mm above the posterior s...

We investigate the hardness of approximating the longest path and the longest cycle in directed graphs on n vertices. We show that neither of these two problems can be polynomial time approximated within n1-ε for any ε > 0 unless P = NP. In particular, the result holds for digraphs of constant bounded outdegree that contain a Hamiltonian cycle. Assuming the stronger complexity conjecture that S...

In multi-hop wireless networks, communication quality depends on the route from a source to a destination. In this paper, we consider a one-dimensional multi-hop wireless network where nodes are distributed randomly and theoretically analyze the relation between communication quality and routing policy using a measure called the Expected Transmission Count (ETX), which is the predicted number o...

Let Tp denote any tetrahedralization of a convex polyhedron P and let G be the dual graph of Tp such that each node of G T corresponds to a tetrahedron of Tp and two nodes are connected by an edge in G T if and only if the two corresponding tetrahedra share a common facet in Tp. Tp is called a Hamiltonian tetrahedralization if G contains a Hamiltonian path (HP). A wellknown open problem in comp...

The 0-1 knapsack problem is an open issue in discrete optimization problems, which plays an important role in real applications. In this paper, a new bio-inspired model is proposed to solve this problem. The proposed method has three main steps. First, the 0-1 knapsack problem is converted into a directed graph by the network converting algorithm. Then, for the purpose of using the amoeboid org...

Abstrac t-Based on an incremental path search algorithm, this paper addresses the problem of performance driven path classification by sizing selected gates on the shortest and the longest identified paths of the circuit. Delay and power/area constraints are managed using circuit path sizing alternatives defined through a realistic evaluation of gate power and delay. Implemented in the POPS too...

Given a set P n of n points on the plane labeled with the integers f1; : : : ; ng, an increasing path of P n is a sequence of points i 1 < : : : < i k such that the polygonal path ob-1 is non-self intersecting. We show that any point set on the plane admits an increasing path of length at least p 2n. We also study the problem of nding the longest common increasing path of two convex point sets ...

We consider digraphs – called extended locally semicomplete digraphs, or extended LSD’s, for short – that can be obtained from locally semicomplete digraphs by substituting independent sets for vertices. We characterize Hamiltonian extended LSD’s as well as extended LSD’s containing Hamiltonian paths. These results as well as some additional ones imply polynomial algorithms for finding a longes...

Each student should select a paper to present to the class and notify Professor Warnow of this selection by e-mail prior to next Tuesday's lecture. Scribe Notes. Beginning with today's lecture, a designated scribe will be responsible for taking notes on each lecture, typesetting a polished and thorough version of the notes in L A T E X, e-mailing the notes in both .tex and .pdf formats to Profe...