Abstract

Computing convex hull for a given set of points is one of the most explored problems in the area of computational geometry (CG). If the set of points is distributed among a set of parties who jointly wish to compute the convex hull, each party can send his points to every other party, and can then locally compute the hull using any of the existing algorithms in CG. However such an approach does not work if the parties wish to compute the convex hull securely, i.e., no party wishes to reveal any of his input points to any other party apart from those that are part of the answer. The problem of secure computation of convex hull for two parties was first introduced by Du and Atallah (NSPW '01). The first solution to the problem was given by Wang et. al(ARES '08). However, the proposed solution was based on well known algorithms for computing convex hull in CG which are proven to be sub-optimal. We propose a new solution for secure computation of convex hull with a considerable improvement in computational complexity. We further show how to extend our two-party protocol for the case of any number of parties.

Abstract

We present a method for finding paths for multiple unmanned air vehicles (UAVs) such that the sum over their lengths is minimum as they cover a 3D terrain (represented as height fields). The paths are constrained to lie beneath an exposure surface to ensure stealth from enemy outposts. The exposure surface is also computed as a height field. The algorithm greedily clusters the terrain such that gain in visibility per distance would be higher for intra-cluster points than points across clusters. Paths generated on clusters formed by such a per distance visibility metric are reduced by more than 25% over other related decoupled methods. The method is extended to cover terrains with partial visibilities. The advantage of the coupled metric extends under constrained visibility also. We again show performance gain by comparing with an existing decoupled algorithm that solves a similar problem of minimum distance terrain coverage with constrained visibility. The paper reveals that decomposing the terrain based on visibility first and then distance is always better than the other way round to cover the terrain in shorter distances.

Abstract

We present a method for finding reduced time coverage paths of multiple UAVs (Unmanned Air Vehicles) monitoring a 3D terrain represented as height fields. A novel metric based on per time visibility is used that couples visibility gained at a terrain point with the time spent to reach the point. This coupled metric is utilized to form reduced time paths by maximizing the visibility gained per unit time at every step. We compare the results of this approach with an approach that covers the terrain based on a per distance visibility metric, which reduces the sum, over distances covered by each UAV path. The comparisons show that the current method gives substantially time reduced paths albeit with an expected increase in sum over distances of UAV paths. We also show that time taken to cover the terrain based on the current metric is far less than prevalent methods that try to decompose the terrain based on visibility followed by time or time followed by visibility in a decoupled fashion. The method is further extended to provide for fault tolerance on a hostile terrain. Each terrain point is guaranteed to be seen by at-least one UAV that has not been damaged due to any calamity, shot or otherwise.

Abstract

We consider the problem of probabilistic reliable communication (PRC) over synchronous networks modeled as directed graphs in the presence of a Byzantine adversary when players’ knowledge of the network topology is not complete. We show that possibility of PRC is extremely sensitive to the changes in players’ knowledge of the topology. This is in complete contrast with earlier known results on the possibility of perfectly reliable communication over undirected graphs where the case of each player knowing only its neighbours gives the same result as the case where players have complete knowledge of the network. Specifically, in either case,(2t+ 1)-vertex connectivity is necessary and sufficient, where t is the number of nodes that can be corrupted by the adversary [DDWY93, SKR+05]. We introduce a novel model for quantifying players’ knowledge of network topology, denoted by T K. Given a directed graph G, influenced by a Byzantine adversary that can corrupt up to any t players, we give a necessary and sufficient condition for possibility of PRC over G for any arbitrary topology knowledge T K. It follows from our main characterization theorem that knowledge of up to d=⌊ n− 2t

Abstract

In this paper, we study the inherent tradeoff between the network connectivity, phase complexity and communication complexity of perfectly reliable message transmission (PRMT) problem in undirected synchronous network, tolerating a mixed adversary A^ b, t,) i who has unbounded computing power and can corrupt£(, and tf nodes in the network in Byzantine and fail-stop fashion respectively.

Abstract

In the problem of USMT [1, 2] 1, a sender S and a receiver R. are connected by n= 2t+ 1 bi-directional synchronous channels (also called as wires) such that any t out of the n channels are corrupted in Byzantine fashion by an adversary jA. t, having unbounded computing power. S intends to communicate a message m to R (where m£ F and I> 1 with F being a finite field) by executing a protocol such that after interacting in terms of phases, 2 R outputs m with probability at least (1—2~") and At gets no information about m. In [2], it shown that in any single phase USMT protocol with n= 2t+ 1,Xi>'J'+ 1, where 5 denotes the message space of S, X, denotes the set of possible data sent through the ith wire and 0< 6<^ is the error probability. 4 In [2], a single phase inefficient USMT protocol with communication complexity approximately matching the above bound has been proposed. We present a single phase polynomial time USMT protocol whose communication complexity is

Abstract

Protocols for Generalized Oblivious Transfer(GOT) were introduced by Ishai and Kushilevitz [10]. They built it by reducing GOT protocols to standard 1-out-of-2 oblivious transfer protocols based on private protocols. In our protocols, we provide alternative reduction by using secret sharing schemes instead of private protocols. We therefore show that there exist a natural correspondence between GOT and general secret sharing schemes and thus the techniques and tools developed for the latter can be applied equally well to the former.

Abstract

(URMT) problem, two non-faulty players, the sender S and the receiver R are part of a synchronous network modeled as a directed graph. S has a message that he wishes to send to R; the challenge is to design a protocol such that after exchanging messages as per the protocol, the receiver R should correctly obtain S’s message with arbitrarily small error probability δ, in spite of the influence of a Byzantine adversary that may actively corrupt up to t nodes in the network (we denote such a URMT protocol as (t,(1− δ))-reliable). While it is known that (2t+ 1) vertex disjoint directed paths from S to R are necessary and sufficient for (t, 1)-reliable URMT (that is with zero error probability), we prove that a strictly weaker condition, which we define and denote as (2t, t)-special-connectivity, together with just (t+ 1) vertex disjoint directed paths from S to R, is necessary and sufficient for (t,(1− δ))-reliable URMT with arbitrarily small (but non-zero) error probability, δ. Thus, we demonstrate the power of randomization in the context of reliable message transmission. In fact, for any positive integer k> 0, we show that there always exists a digraph Gk such that (k, 1)-reliable URMT is impossible over Gk whereas there exists a (2k,(1− δ))-reliable URMT protocol, δ> 0 in Gk. In a digraph G on which (t,(1− δ))-reliable URMT is possible, an edge is called critical if the deletion of that edge renders (t,(1− δ))-reliable URMT impossible. We give an example of a digraph G on n vertices such that G has Ω (n2) critical edges. This is quite baffling since no such graph exists for the case of perfect reliable message transmission (or equivalently (t, 1)-reliable URMT) or when the underlying graph is undirected. Such is the anomalous behavior of URMT protocols (when “randomness meet directedness”) that it makes it extremely hard to design efficient protocols over arbitrary digraphs. However, if URMT is possible between every pair of vertices in the network, then we present efficient protocols for the same.

Abstract

For content level access, very often database needs the query as a sample image. However, the image may contain private information and hence the user does not wish to reveal the image to the database. Private content based image retrieval (PCBIR) deals with retrieving similar images from an image database without revealing the content of the query image - not even to the database server. We propose algorithms for PCBIR, when the database is indexed using hierarchical index structure or hash based indexing scheme. Experiments are conducted on real datasets with popular features and state of the art data structures. It is observed that specialty and subjectivity of image retrieval (unlike SQL queries to a relational database) enables in computationally efficient yet private solutions.

Abstract

In this paper we present an automatic Keyphrase extraction technique for English documents of scientific domain. The devised algorithm uses n-gram filtration technique, which filters sophisticated n-grams {1dnd4} along with their weight from the words of input document. To develop n-gram filtration technique, we have used (1) LZ78 data compression based technique, (2) a simple refinement step, (3) A simple Pattern Filtration algorithm and, (4) a term weighting scheme. In term weighting scheme, we have introduced the importance of position of sentence (where given phrase occurs first) in document and position of phrase in sentence for documents of scientific domain (which is literally more organized than other domains). The entire system is based upon statistical observations, simple grammatical facts, heuristics, and lexical information of English language. We remark that the devised system does not require a learning phase. Our experimental results with publically available text dataset, shows that the devised system is comparable with other known algorithms.