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For a fixed integer k ≥ 0, a k-transmitter is an omnidirectional wireless transmitter with an infinite broadcast range that is able to penetrate up to k “walls”, represented as line segments in the plane. We develop lower and upper bounds for the number of k-transmitters that are necessary and sufficient to cover a given collection of line segments, polygonal chains and polygons.
The minimum spanning tree problem is one of the most fundamental algorithmic graph problems and OBDDs are a very common dynamic data structure for Boolean functions. Since in some applications graphs become larger and larger, a research branch has emerged which is concerned with the design and analysis of so-called symbolic algorithms for classical graph problems on OBDD-represented graph instances...
This paper studies the selfish routing game in ring networks with a load-dependent linear latency on each link. We adopt the asymmetric atomic routing model. Each player selfishly chooses a route to connect his source-destination pair, aiming at a lowest latency of his route, while the system objective is to minimize the maximum latency among all routes of players. Such a routing game always has a...
One approach to guarantee the performance of underwater acoustic sensor networks is to deploy multiple Surface-level Gateways (SGs) at the surface. This paper addresses the connected (or survivable) Constrained Surface-level Gateway Placement (C-SGP) problem for 3-D underwater acoustic sensor networks. Given a set of candidate locations where SGs can be placed, our objective is to place minimum number...
In a network environments supporting mobile entities (called robots or agents), a black hole is harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problem is the task of a team of k > 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this...
Given a set S of n sensors in the plane we consider the problem of establishing an ad hoc network from these sensors using directional antennae. We prove that for each given integer 1 ≤ k ≤ 5 there is a strongly connected spanner on the set of points so that each sensor uses at most k such directional antennae whose range differs from the optimal range by a multiplicative factor of at most $2...
In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work [7] shows that this problem has no fully polynomial time approximation schemes unless P = NP. We present a polynomial time algorithm yielding a PageRank value within a constant...
Query evaluation in an XML database requires reconstructing XML subtrees rooted at nodes found by an XML query. Since XML subtree reconstruction can be expensive, one approach to improve query response time is to use reconstruction views - materialized XML subtrees of an XML document, whose nodes are frequently accessed by XML queries. For this approach to be efficient, the principal requirement is...
The connected dominating set (CDS) problem is a well studied NP-hard problem with many important applications. Dorn et al. [ESA2005, LNCS3669,pp95-106] introduce a new technique to generate $2^{O(\sqrt{n})}$ time and fixed-parameter algorithms for a number of non-local hard problems, including the CDS problem in planar graphs. The practical performance of this algorithm is yet to be evaluated...
The classical and well-studied group testing problem is to find d defectives in a set of n elements by group tests, which tell us for any chosen subset whether it contains defectives or not. Strategies are preferred that use both a small number of tests close to the information-theoretic lower bound dlogn, and a small constant number of stages, where tests in every stage are done in parallel, in order...
Experts working for railway operators still have to devote much time and effort to creating plans for rolling stock allocation. In this paper, we formulate the railway rolling stock allocation problem as a set partitioning multi-commodity flow (SPMCF) problem and we propose a search-based heuristic approach for SPMCF. We show that our approach can obtain an approximate solution near the optimum in...
Given a directed graph G with non negative cost on the arcs, a directed tree cover of G is a rooted directed tree such that either head or tail (or both of them) of every arc in G is touched by T. The minimum directed tree cover problem (DTCP) is to find a directed tree cover of minimum cost. The problem is known to be NP-hard. In this paper, we show that the weighted Set Cover Problem (SCP) is a...
A spanning subgraph of a given graph G is called a spanning star forest of G if it is a collection of node-disjoint trees of depth at most 1 (such trees are called stars). The size of a spanning star forest is the number of leaves in all its components. The goal of the spanning star forest problem [12] is to find the maximum-size spanning star forest of a given graph. In this paper, we study...
We give a sufficient condition, which guarantees that for arbitrary Hamiltonian cycle C, there exists a [k,k + 1]-factor containing C. This improves a previous result of Cai, Li, and Kano [7].
The Yao and Theta graphs are defined for a given point set and a fixed integer k > 0. The space around each point is divided into k cones of equal angle, and each point is connected to a nearest neighbor in each cone. The difference between Yao and Theta graphs is in the way the nearest neighbor is defined: Yao graphs minimize the Euclidean distance between a point and its neighbor, and Theta graphs...
The best known expected time for the all pairs shortest path problem on a directed graph with non-negative edge costs is O(n2logn) by Moffat and Takaoka. Let the solution set be the set of vertices to which the given algorithm has established shortest paths. The Moffat-Takaoka algorithm maintains complexities before and after the critical point in balance, which is the moment when the size...
A distance-k matching in a graph G is matching M in which the distance between any two edges of M is at least k. A distance-2 matching is more commonly referred to as an induced matching. In this paper, we show that when G is weakly chordal, the size of the largest induced matching in G is equal to the minimum number of co-chordal subgraphs of G needed to cover the edges of G, and that the co-chordal...
Given an undirected graph G = (V,E) with positive edge weights and two vertices s and t, the next-to-shortest path problem is to find an st-path which length is minimum among all st-paths of lengths strictly larger than the shortest path length. In this paper we give an O(|V|log|V| + |E|) time algorithm for this problem, which improves the previous result of O(|V|2) time for sparse graphs.
Given a graph G = (V,E) in which a fugitive hides on vertices or along edges, graph searching problems are usually to find the minimum number of searchers required to capture the fugitive. In this paper, we consider the problem of finding the minimum number of steps to capture the fugitive. We introduce the fast edge-searching problem in the edge search model, which is the problem of finding the minimum...
Given an edge-weighted undirected graph G = (V,E,c,w), where each edge e ∈ E has a cost c(e) and a weight w(e), a set S ⊆ V of terminals and a positive constant D0, we seek a minimum cost Steiner tree where all terminals appear as leaves and its diameter is bounded by D0. Note that the diameter of a tree represents the maximum weight of path connecting two different leaves in...
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