We consider ad hoc wireless networks that are configured as Mobile Backbone Networks. A hierarchical network architecture is synthesized, consisting of Access Nets (ANets) and Backbone Nets (BNets). Each ANet is manag...
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We consider ad hoc wireless networks that are configured as Mobile Backbone Networks. A hierarchical network architecture is synthesized, consisting of Access Nets (ANets) and Backbone Nets (BNets). Each ANet is managed by a (dynamically elected) Backbone Node (BN) that is equipped with higher capability (transmission and processing) modules. The BNs are chosen from currently active mobile backbone-capable nodes or are represented by (ground and/or airborne) unmanned vehicles (UVs) that are guided into selected positions. In this paper, we develop and investigate a new joint power controlled medium access control (MAC) algorithm for wireless access nets (ANets). Under our new protocol, the net backbone node instructs the ANet nodes to make power control adjustments while simultaneously allocating to them slots for the requested transmissions of their packets. This algorithm, in contrast to other employed conventional graph-based scheduling algorithms, satisfies the requirement that a minimum signal-to-interference and noise ratio (SINR) is met at all intended receivers. We show our algorithm to lead to a significant increase in the net throughput level by attaining high spatial reuse.
An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the in...
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An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique numbers omega(1)(v) and omega(2)(v) at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than [5omega(G)/4] + 3 colors for any triangle-free hexagonal graph G, without explicitly computing the global clique number omega(G). Hence the competitive ratio of the algorithm is 5/4. (C) 2004 Elsevier B.V. All rights reserved.
We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case ...
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We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure. The main result of the article is the analysis of a popular spectral algorithm. One variant of spectral clustering turns out to have effective worst-case guarantees;another finds a "good" clustering, if one exists.
It is known that the acyclic chromatic number of a subcubic graph is at most four, and its acyclic edge chromatic number is at most five. We present algorithms that prove these two facts. Let n be the number of vertic...
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It is known that the acyclic chromatic number of a subcubic graph is at most four, and its acyclic edge chromatic number is at most five. We present algorithms that prove these two facts. Let n be the number of vertices of a graph. Our first algorithm takes O(n) time and uses four colors to properly color the vertices of any subcubic graph so that there is no 2-colored cycle. Our second algorithm takes O(n) time and uses five colors to properly color the edges of any subcubic graph so that there is no 2-colored cycle. Both are the first linear-time algorithms for the problems they solve. (C) 2004 Elsevier B.V. All rights reserved.
A bull is a graph with five vertices a, b, c, d, e and five edges ab, ac, bc, da, eb. Here we present polynomial-time combinatorial algorithms for the optimal weighted coloring and weighted clique problems in bull-fre...
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A bull is a graph with five vertices a, b, c, d, e and five edges ab, ac, bc, da, eb. Here we present polynomial-time combinatorial algorithms for the optimal weighted coloring and weighted clique problems in bull-free perfect graphs. The algorithms are based on a structural analysis and decomposition of bull-free perfect graphs.
We address the problem of deciding whether a given network is stable in the Adversarial Queueing Model when considering farthest-from-source (FFS) as the queueing policy to schedule the packets through its links. We s...
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We address the problem of deciding whether a given network is stable in the Adversarial Queueing Model when considering farthest-from-source (FFS) as the queueing policy to schedule the packets through its links. We show a characterisation of the networks which are stable under FFS in terms of a family of forbidden subgraphs. We show that the set of networks stable under FFS coincide with the set of universally stable networks. Since universal stability of networks can be checked in polynomial time, we obtain that stability under FFS can also be decided in polynomial time. (C) 2004 Elsevier B.V. All rights reserved.
We show that the step domination number of any tree T satisfies gamma(S) less than or equal to ((5)/(6) + O(1/D))n, where n is the number of vertices of T, and D is its diameter. It is also proved that if some require...
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We show that the step domination number of any tree T satisfies gamma(S) less than or equal to ((5)/(6) + O(1/D))n, where n is the number of vertices of T, and D is its diameter. It is also proved that if some requirements are set on a tree T then, gamma(S)(T) less than or equal to O(D). (C) 2004 Elsevier B.V. All rights reserved.
A radio labeling of a graph G is an assignment of pairwise distinct, positive integer labels to the vertices of G such that labels of adjacent vertices differ by at least 2. The radio labeling problem (RL) consists in...
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A radio labeling of a graph G is an assignment of pairwise distinct, positive integer labels to the vertices of G such that labels of adjacent vertices differ by at least 2. The radio labeling problem (RL) consists in determining a radio labeling that minimizes the maximum label that is used (the so-called span of the labeling). RL is a well-studied problem, mainly motivated by frequency assignment problems in which transmitters are not allowed to operate on the same frequency channel. We consider the special case where some of the transmitters have preassigned operating frequency channels. This leads to the natural variants p-RL(l) and p-RL(*) of RL with l preassigned labels and an arbitrary number of preassigned labels, respectively. We establish a number of combinatorial, algorithmical, and complexity-theoretical results for these variants of radio labeling. In particular, we investigate a simple upper bound on the minimum span, yielding a linear time approximation algorithm with a constant additive error bound for p-RL(*) restricted to graphs with girth greater than or equal to 5. We consider the complexity of p-RL( l) and p-RL(*) for several cases in which RL is known to be polynomially solvable. On the negative side, we prove that p-RL(*) is NP-hard for cographs and for k-colorable graphs where a k-coloring is given (k greater than or equal to 3). On the positive side, we derive polynomial time algorithms solving p-RL(*) and p-RL(l) for graphs with bounded maximum degree, and for solving p-RL(l) for k-colorable graphs where a k-coloring is given.
A tree (tour) cover of an edge-weighted graph is a set of edges which forms a tree (closed walk) and covers every other edge in the graph. Arkin et al. [1] give approximation algorithms with ratios 3.55 (tree cover) a...
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A tree (tour) cover of an edge-weighted graph is a set of edges which forms a tree (closed walk) and covers every other edge in the graph. Arkin et al. [1] give approximation algorithms with ratios 3.55 (tree cover) and 5.5 (tour cover). We present algorithms with a worst-case ratio of 3 for both problems.
Maximum Residual Energy Path (MREP) routing has been shown an effective routing scheme for energy conservation in battery powered wireless networks. Past studies on MREP routing are based on the assumption that the tr...
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Maximum Residual Energy Path (MREP) routing has been shown an effective routing scheme for energy conservation in battery powered wireless networks. Past studies on MREP routing are based on the assumption that the transmitting node consumes power, but the receiving node does not. This assumption is false if acknowledgment is required as occurs, for example, in some Bluetooth applications. If the receiving node does not consume power then the MREP routing problem for a single message is easily solvable in polynomial time using a simple Dijkstra-like algorithm. We further show in that when the receiving node does consume power the problem becomes NP-complete and is even impossible to approximate with an exponential approximation factor in polynomial time unless P = NP. (C) 2003 Elsevier B.V. All rights reserved.
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