Experimental study of geometric t-spanners : a running time comparison

The construction of t-spanners of a given point set has received a lot of attention, especially from a theoretical perspective. We experimentally study the performance of the most common construction algorithms for points in the Euclidean plane. In a previous paper [10] we considered the properties of the produced graphs from five common algorithms. We consider several additional algorithms and focus on the running times. This is the first time an extensive comparison has been made between the running times of construction algorithms of t-spanners

Clinical activity of ipilimumab for metastatic uveal melanoma: a retrospective review of the Dana-Farber Cancer Institute, Massachusetts General Hospital, Memorial Sloan-Kettering Cancer Center, and University Hospital of Lausanne experience.

BACKGROUND: Uveal melanoma exhibits a high incidence of metastases; and, to date, there is no systemic therapy that clearly improves outcomes. The anticytotoxic T-lymphocyte-associated protein 4 (anti-CTLA-4) antibody ipilimumab is a standard of care for metastatic melanoma; however, the clinical activity of CTLA-4 inhibition in patients with metastatic uveal melanoma is poorly defined. METHODS: To assess ipilimumab in this setting, the authors performed a multicenter, retrospective analysis of 4 hospitals in the United States and Europe. Clinical characteristics, toxicities, and radiographic disease burden, as determined by central, blinded radiology review, were evaluated. RESULTS: Thirty-nine patients with uveal melanoma were identified, including 34 patients who received 3 mg/kg ipilimumab and 5 who received 10 mg/kg ipilimumab. Immune-related response criteria and modified World Health Organization criteria were used to assess the response rate (RR) and the combined response plus stable disease (SD) rate after 12 weeks, after 23 weeks, and overall (median follow-up, 50.4 weeks [12.6 months]). At week 12, the RR was 2.6%, and the response plus SD rate was 46.%; at week 23, the RR was 2.6%, and the response plus SD rate was 28.2%. There was 1 complete response and 1 late partial response (at 100 weeks after initial SD) for an immune-related RR of 5.1%. Immune-related adverse events were observed in 28 patients (71.8%) and included 7 (17.9%) grade 3 and 4 events. Immune-related adverse events were more frequent in patients who received 10 mg/kg ipilimumab than in those who received 3 mg/kg ipilimumab. The median overall survival from the first dose of ipilimumab was 9.6 months (95% confidence interval, 6.3-13.4 months; range, 1.6-41.6 months). Performance status, lactate dehydrogenase level, and an absolute lymphocyte count ≥ 1000 cells/μL at week 7 were associated significantly with survival. CONCLUSIONS: In this multicenter, retrospective analysis of 4 hospitals in the United States and Europe of patients with uveal melanoma, durable responses to ipilimumab and manageable toxicity were observed

An optimal algorithm for computing angle-constrained spanners

Let S be a set of n points in ℝd. A graph G = (S,E) is called a t-spanner for S, if for any two points p and q in S, the shortest-path distance in G between p and q is at most t|pq|, where |pq| denotes the Euclidean distance between p and q. The graph G is called θ-angle-constrained, if any two distinct edges sharing an endpoint make an angle of at least θ. It is shown that, for any θ with 0 < θ < π/3, a θ-angle-constrained t-spanner can be computed in O(n logn) time, where t depends only on θ

The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition

A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good spanners 'emerge' in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. Our main result is to show that if edges are built in an arbitrary order but an edge is built if and only if its endpoints are not 'close' to the endpoints of an existing edge, the graph is a (1 + \eps)-spanner with a linear number of edges, constant average degree, and the total edge length as a small logarithmic factor of the cost of the minimum spanning tree. As a side product, we show a simple greedy algorithm for constructing optimal size well-separated pair decompositions that may be of interest on its own

I/O-efficient shortest path queries in geometric spanners

Abstract. We present I/O-efficient algorithms to construct planar Steiner spanners for point sets and sets of polygonal obstacles in the plane, and for constructing the “dumbbell ” spanner of [6] for point sets in higher dimensions. As important ingredients to our algorithms, we present I/O-efficient algorithms to color the vertices of a graph of bounded degree, answer binary search queries on topology buffer trees, and preprocess a rooted tree for answering prioritized ancestor queries.