Random Geometric Problems on 0; 1] 2
نویسنده
چکیده
In this paper we survey the work done for graphs on random geometric models. We present some heuristics for the problem of the Minimal Linear Arrangement on 0; 1] 2 and we conclude with a collection of open problems.
منابع مشابه
Two-boundary Problems for a Random Walk with Negative Geometric Jumps
Two-boundary problems for a random walk with negative geometric jumps are considered, and the corresponding results for a usual semicontinuous random walk are generalized for them. The following results are obtained: the probability distribution of ruin is found and expressed in terms of the lower and upper boundaries; formulas are given for the joint distribution of the infimum, supremum, and ...
متن کاملEstimators and tail bounds for dimension reduction in lα (0 < α ≤ 2) using stable random projections
Abstract The method of stable random projections is popular in data stream computations, data mining, information retrieval, and machine learning, for efficiently computing the lα (0 < α ≤ 2) distances using a small (memory) space, in one pass of the data. We propose algorithms based on (1) the geometric mean estimator, for all 0 < α ≤ 2, and (2) the harmonic mean estimator, only for small α (e...
متن کاملConnectivity Threshold of Random Geometric Graphs with Cantor Distributed Vertices
For connectivity of random geometric graphs, where there is no density for underlying distribution of the vertices, we consider n i.i.d. Cantor distributed points on [0, 1]. We show that for this random geometric graph, the connectivity threshold Rn, converges almost surely to a constant 1−2φ where 0 < φ < 1/2, which for standard Cantor distribution is 1/3. We also show that ‖Rn − (1− 2φ)‖1 ∼ 2...
متن کاملLinear Orderings of Random Geometric Graphs
In random geometric graphs, vertices are randomly distributed on [0, 1] and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cu...
متن کاملOn random walks
4.* Use 3. to show that the average number of visits to a > 0 before returning to the origin is 1 (hint: show that it is closely related to the expectation of some geometric random variable). Solution: let Na be the number of visits to a before returning to 0. Using question 3. one has P(Na = 0) = 1 2 + 1 2 (1− 1/a) (call that probability q). Note that once you’ve made a visit to a (that is giv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998