On One-Round Discrete Voronoi Games

Let V be a multiset of n points in R^d, which we call voters, and let k >=slant 1 and l >=slant 1 be two given constants. We consider the following game, where two players P and Q compete over the voters in V: First, player P selects a set P of k points in R^d, and then player Q selects a set Q of l points in R^d. Player P wins a voter v in V iff dist(v,P) <=slant dist(v,Q), where dist(v,P) := min_{p in P} dist(v,p) and dist(v,Q) is defined similarly. Player P wins the game if he wins at least half the voters. The algorithmic problem we study is the following: given V, k, and l, how efficiently can we decide if player P has a winning strategy, that is, if P can select his k points such that he wins the game no matter where Q places her points. Banik et al. devised a singly-exponential algorithm for the game in R^1, for the case k=l. We improve their result by presenting the first polynomial-time algorithm for the game in R^1. Our algorithm can handle arbitrary values of k and l. We also show that if d >= 2, deciding if player P has a winning strategy is Sigma_2^P-hard when k and l are part of the input. Finally, we prove that for any dimension d, the problem is contained in the complexity class exists for all R, and we give an algorithm that works in polynomial time for fixed k and l

Fast Fencing

We consider very natural "fence enclosure" problems studied by Capoyleas, Rote, and Woeginger and Arkin, Khuller, and Mitchell in the early 90s. Given a set $S$ of $n$ points in the plane, we aim at finding a set of closed curves such that (1) each point is enclosed by a curve and (2) the total length of the curves is minimized. We consider two main variants. In the first variant, we pay a unit cost per curve in addition to the total length of the curves. An equivalent formulation of this version is that we have to enclose $n$ unit disks, paying only the total length of the enclosing curves. In the other variant, we are allowed to use at most $k$ closed curves and pay no cost per curve. For the variant with at most $k$ closed curves, we present an algorithm that is polynomial in both $n$ and $k$. For the variant with unit cost per curve, or unit disks, we present a near-linear time algorithm. Capoyleas, Rote, and Woeginger solved the problem with at most $k$ curves in $n^{O(k)}$ time. Arkin, Khuller, and Mitchell used this to solve the unit cost per curve version in exponential time. At the time, they conjectured that the problem with $k$ curves is NP-hard for general $k$. Our polynomial time algorithm refutes this unless P equals NP

Minimum Perimeter-Sum Partitions in the Plane

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P_1 and P_2 such that the sum of the perimeters of CH(P_1) and CH(P_2) is minimized, where CH(P_i) denotes the convex hull of P_i. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n^2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log^4 n) time and a (1+e)-approximation algorithm running in O(n + 1/e^2 log^4(1/e)) time

Range-Clustering Queries

In a geometric k-clustering problem the goal is to partition a set of points in R^d into k subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering queries on a point set S: given a query box Q and an integer k > 2, compute an optimal k-clustering for the subset of S inside Q. We obtain the following results. * We present a general method to compute a (1+epsilon)-approximation to a range-clustering query, where epsilon>0 is a parameter that can be specified as part of the query. Our method applies to a large class of clustering problems, including k-center clustering in any Lp-metric and a variant of k-center clustering where the goal is to minimize the sum (instead of maximum) of the cluster sizes. * We extend our method to deal with capacitated k-clustering problems, where each of the clusters should not contain more than a given number of points. * For the special cases of rectilinear k-center clustering in R^1, and in R^2 for k = 2 or 3, we present data structures that answer range-clustering queries exactly

Path Planning for Image-based Control of Wheeled Mobile Manipulators

Abstract—We address the problem of incorporating path planning with image-based control of a wheeled mobile manipulator (WMM) performing visually-guided tasks in complex environments.TheWMMconsistsofawheeled(non-holonomic) mobile platform and an on-board robotic arm equipped with a camera mounted at its end-effector. The visually-guided task is to move the WMM from an initial to a desired location while respecting image and physical constraints. We propose a kinodynamic planning approach that explores the camera state space for permissible trajectories by iteratively extending a search tree in this space and simultaneously tracking these trajectories in the WMM configuration space. We utilize weighted pseudo-inverse Jacobian solutions combined with a null space optimization technique to effectively coordinate the motion of the mobile platform and the arm. We also present the preliminary results obtained by executing the planned trajectories on a real WMM system via a decoupled control scheme where the on-board arm is servo controlled along the planned feature trajectories while the mobile platform is simultaneously controlled along its trajectory using a state feedback tracking method. I

Faster algorithms for computing plurality points

Let V be a set of n points in R d, which we call voters. A point p ∈ R d is preferred over another point p' ∈ R d by a voter v ∈ V if dist(v, p) < dist(v, p'). A point p is called a plurality point if it is preferred by at least as many voters as any other point p'. We present an algorithm that decides in O(n log n) time whether V admits a plurality point in the L 2 norm and, if so, finds the (unique) plurality point. We also give efficient algorithms to compute a minimum-cost subset W ⊂ V such that V \ W admits a plurality point, and to compute a so-called minimum-radius plurality 6 ball. Finally, we consider the problem in the personalized L 1 norm, where each point v ∈ V has a preference vector w 1 (v), . . ., w d (v) and the distance from v to any point p ∈ R d is given by d i= 1 w i (v) · |x i (v) − x i (p) |. For this case we can compute in O(n d −1 ) time the set of all plurality points of V. When all preference vectors are equal, the running time improves to O(n)

Comparison of the Effectiveness of Progressive Relaxation and Abdominal Breathing Technique on Pain Anxiety of Burning Deressing

Background and Aim: Burned patients experience a high level of anxiety during dress changing. The use of complementary medicine is one of the methods of anxiety management that many studies have conducted about it in recent years. The purpose of this study was to compare the effectiveness of progressive relaxation with abdominal respiration technique on pain‌‌ anxiety of burn dressing.  Materials and Methods: This study was a randomized clinical trial with a control group. We selected forty-five patients referred to Zare Hospital in Sari through simple sampling and assigned into three groups. The first group received relaxation intervention, the second group received respiratory technique intervention, and no intervention was performed in the control group. Burn Specific Pain Anxiety Scale (BSPAS) was used to measure pain-related anxiety. SPSS software version 20 was used to analyze the data. Descriptive statistics, ANOVA and Tukey’s post hoc test were used for data analysis. Results: Based on the results, 28% of the participants in the study were single and 72% were married. In terms of age, most of the participants were between 31 and 40 years old. The findings showed that there was no significant difference between the mean pain anxiety levels in the three groups before the intervention. There was a significant difference in the average burn dressing pain anxiety after the intervention between the relaxation group and the control group (P<0.001) and the breathing techniques group and the control group (P<0.000), so that the average burn dressing pain anxiety in the group Relaxation was reduced by 8.60 units as compared to the control group and in the breathing techniques group by 11.60 units as compared to the control group. Conclusions: The use of relaxation “techniques” and respiratory techniques, which are non-pharmacological methods, are recommended during dress changing in the burned patient. These methods are simple and inexpensive and can reduce the effects of pain anxiety during dress changing

Minimum perimeter-sum partitions in the plane

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P1 and P2 such that the sum of the perimeters of CH(P1) and CH(P2) is minimized, where CH(Pi) denotes the convex hull of Pi. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(nlog 2n) time and a (1 + ε) -approximation algorithm running in O(n+ 1 / ε2· log 2(1 / ε)) time

The CSL112-2001 trial: Safety and tolerability of multiple doses of CSL112 (apolipoprotein A-I [human]), an intravenous formulation of plasma-derived apolipoprotein A-I, among subjects with moderate renal impairment after acute myocardial infarction

International audienceBACKGROUND:CSL112 (apolipoprotein A-I [human]) is a plasma-derived apolipoprotein A-I developed for early reduction of cardiovascular risk following an acute myocardial infarction (AMI). The safety of CSL112 among AMI subjects with moderate, stage 3 chronic kidney disease (CKD) is unknown.METHODS:CSL112_2001, a multicenter, placebo-controlled, parallel-group, double-blind, randomized phase 2 trial, enrolled patients with moderate CKD within 7 days following AMI. Enrollment was stratified on the basis of estimated glomerular filtration rate and presence of diabetes requiring treatment. Patients were randomized in a 2:1 ratio to receive 4 weekly infusions of CSL112 6 g or placebo. The co-primary safety end points were renal serious adverse events (SAEs) and acute kidney injury, defined as an increase ≥26.5 μmol/L in baseline serum creatinine for more than 24 hours, during the treatment period.RESULTS:A total of 83 patients were randomized (55 CSL112 vs 28 placebo). No increase in renal SAEs was observed in the CSL112 group compared with placebo (CSL112 = 1 [1.9%], placebo = 4 [14.3%]). Similarly, no increase in acute kidney injury events was observed (CSL112 = 2 [4.0%], placebo = 4 [14.3%]). Rates of other SAEs were similar between groups. CSL112 administration resulted in increases in ApoA-I and cholesterol efflux similar to those observed in patients with AMI and normal renal function or stage 2 CKD enrolled in the ApoA-I Event Reducing in Ischemic Syndromes I trial.CONCLUSIONS:These results demonstrate the acceptable safety of the 6-g dose of CSL112 among AMI subjects with moderate stage 3 CKD and support inclusion of these patients in a phase 3 cardiovascular outcomes trial powered to assess efficacy