The Maximum Exposure Problem

Given a set of points P and axis-aligned rectangles R in the plane, a point p in P is called exposed if it lies outside all rectangles in R. In the max-exposure problem, given an integer parameter k, we want to delete k rectangles from R so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in R are translates of two fixed rectangles. However, if R only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For general rectangle range space, we present a simple O(k) bicriteria approximation algorithm; that is by deleting O(k^2) rectangles, we can expose at least Omega(1/k) of the optimal number of points

Security Challenges when Space Merges with Cyberspace

Spaceborne systems, such as communication satellites, sensory, surveillance, GPS and a multitude of other functionalities, form an integral part of global ICT cyberinfrastructures. However, a focussed discourse highlighting the distinctive threats landscape of these spaceborne assets is conspicuous by its absence. This position paper specifically considers the interplay of Space and Cyberspace to highlight security challenges that warrant dedicated attention in securing these complex infrastructures. The opinion piece additionally adds summary opinions on (a) emerging technology trends and (b) advocacy on technological and policy issues needed to support security responsiveness and mitigation

Shortest Paths in the Plane with Obstacle Violations

We study the problem of finding shortest paths in the plane among h convex obstacles, where the path is allowed to pass through (violate) up to k obstacles, for k <= h. Equivalently, the problem is to find shortest paths that become obstacle-free if k obstacles are removed from the input. Given a fixed source point s, we show how to construct a map, called a shortest k-path map, so that all destinations in the same region of the map have the same combinatorial shortest path passing through at most k obstacles. We prove a tight bound of Theta(kn) on the size of this map, and show that it can be computed in O(k^2 n log n) time, where n is the total number of obstacle vertices

Supporting Domain-Specific State Space Reductions through Local Partial-Order Reduction

Model checkers offer to automatically prove safety and liveness properties of complex concurrent software systems, but they are limited by state space explosion. Partial-Order Reduction (POR) is an effective technique to mitigate this burden. However, applying existing notions of POR requires to verify conditions based on execution paths of unbounded length, a difficult task in general. To enable a more intuitive and still flexible application of POR, we propose local POR (LPOR). LPOR is based on the existing notion of statically computed stubborn sets, but its locality allows to verify conditions in single states rather than over long paths. As a case study, we apply LPOR to message-passing systems. We implement it within the Java Pathfinder model checker using our general Java-based LPOR library. Our experiments show significant reductions achieved by LPOR for model checking representative message-passing protocols and, maybe surprisingly, that LPOR can outperform dynamic POR. © 2011 IEEE

Improved Approximation Bounds for the Minimum Constraint Removal Problem

In the minimum constraint removal problem, we are given a set of geometric objects as obstacles in the plane, and we want to find the minimum number of obstacles that must be removed to reach a target point t from the source point s by an obstacle-free path. The problem is known to be intractable, and (perhaps surprisingly) no sub-linear approximations are known even for simple obstacles such as rectangles and disks. The main result of our paper is a new approximation technique that gives O(sqrt{n})-approximation for rectangles, disks as well as rectilinear polygons. The technique also gives O(sqrt{n})-approximation for the minimum color path problem in graphs. We also present some inapproximability results for the geometric constraint removal problem

Computing Shortest Paths in the Plane with Removable Obstacles

We consider the problem of computing a Euclidean shortest path in the presence of removable obstacles in the plane. In particular, we have a collection of pairwise-disjoint polygonal obstacles, each of which may be removed at some cost c_i > 0. Given a cost budget C > 0, and a pair of points s, t, which obstacles should be removed to minimize the path length from s to t in the remaining workspace? We show that this problem is NP-hard even if the obstacles are vertical line segments. Our main result is a fully-polynomial time approximation scheme (FPTAS) for the case of convex polygons. Specifically, we compute an (1 + epsilon)-approximate shortest path in time O({nh}/{epsilon^2} log n log n/epsilon) with removal cost at most (1+epsilon)C, where h is the number of obstacles, n is the total number of obstacle vertices, and epsilon in (0, 1) is a user-specified parameter. Our approximation scheme also solves a shortest path problem for a stochastic model of obstacles, where each obstacle\u27s presence is an independent event with a known probability. Finally, we also present a data structure that can answer s-t path queries in polylogarithmic time, for any pair of points s, t in the plane