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We consider the following problem: Given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which needs O(n log k + k log n) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a… (More)

We consider the problem of tracking n targets in the plane using 2n cameras, where tracking each target requires two distinct cameras. A single camera (modeled as a point) sees a target point in a certain direction, ideally with unlimited precision, and thus two cameras (not collinear with the target) unambiguously determine the position of the target. In… (More)

The efficient distributed construction of a maximal independent set (MIS) of a graph is of fundamental importance. We study the problem in the class of Growth-Bounded Graphs, which includes for example the well-known Unit Disk Graphs. In contrast to the fastest (time-optimal) existing approach [11], we assume that no geometric information (e.g., distances… (More)

Context: In order to ensure high quality of a process model repository, refactoring operations can be applied to correct anti-patterns, such as overlap of process models, inconsistent labeling of activities and overly complex models. However, if a process model collection is created and maintained by different people over a longer period of time, manual… (More)

We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simply-or multiply-connected) polygonal workspace, and a moving point-robot whose sensory input at any location is a binary vector representing the cyclic order of the polygon vertices… (More)

Communication in networks suffers if a link fails. When the links are edges of a tree that has been chosen from an underlying graph of all possible links, a broken link even disconnects the network. Most often, the link is restored rapidly. A good policy to deal with this sort of transient link failures is swap rerouting, where the temporarily broken link… (More)

In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum travel time of messages. When a transient failure disables an edge of the MDST, the network is disconnected, and a temporary replacement edge must be chosen, which should ideally minimize the diameter of the… (More)

We present a distributed algorithm for finding a (1 + ε)-approximation of a Minimum Connected Dominating Set in the class of Growth-Bounded graphs, which includes Unit Disk graphs. In addition, the computed Connected Dominating Set guarantees a constant stretch factor on the length of a shortest path with respect to the original graph and induces a subgraph… (More)

In a densely connected communication network, represented by a graph G with nonnegative edge-weights, it is often advantageous to route all communication on a sparse, spanning subnetwork, typically a spanning tree of G. With the communication overhead in mind, we consider a spanning tree T of G which guarantees that for any two nodes, their distance in T is… (More)