Melih Onus

Constant density spanners for wireless ad-hoc networks

An important problem for wireless ad hoc networks has been todesign overlay networks that allow time- and energy-efficientrouting. Many local-control strategies for maintaining such overlaynetworks have already been suggested, but most of them are based onan oversimplified wireless communication model. In this paper, we suggest a model that is much more general thanprevious models. It allows the path loss of transmissions tosignificantly deviate from the idealistic unit disk model and doesnot even require the path loss to form a metric. Also, our model isapparently the first proposed for algorithm design that does notonly model transmission and interference issues but also aims atproviding a realistic model for physical carrier sensing. Physicalcarrier sensing is needed so that our protocols do not require<i>any</i> prior information (not even an estimate onthe number of nodes) about the wireless network to runefficiently. Based on this model, we propose a local-control protocol forestablishing a constant density spanner among a set of mobilestations (or <i>nodes</i>) that are distributed in anarbitrary way in a 2-dimensional Euclidean space. More precisely,we establish a backbone structure by efficiently electing clusterleaders and gateway nodes so that there is only a constant numberof cluster leaders and gateway nodes within the transmission rangeof any node and the backbone structure satisfies the properties ofa topological spanner. Our protocol has the advantage that it is locallyself-stabilizing, i.e., it can recover from <i>any</i>initial configuration, even if adversarial nodes participate in it,as long as the honest nodes sufficiently far away from adversarialnodes can in principle form a single connected component.Furthermore, we only need constant size messages and a constantamount of storage at the nodes, irrespective of the distribution ofthe nodes. Hence, our protocols would even work in extremesituations such as very simple wireless devices (like sensors) in ahostile environment.

Minimum maximum-degree publish-subscribe overlay network design

Designing an overlay network for publish/subscribe communication in a system where nodes may subscribe to many different topics of interest is of fundamental importance. For scalability and efficiency, it is important to keep the degree of the nodes in the publish/subscribe system low. It is only natural then to formalize the following problem: Given a collection of nodes and their topic subscriptions, connect the nodes into a graph that has least possible maximum degree in such a way that for each topic t, the graph induced by the nodes interested in t is connected. We present the first polynomial-time logarithmic approximation algorithm for this problem and prove an almost tight lower bound on the approximation ratio. Our experimental results show that our algorithm drastically improves the maximum degree of publish/subscribe overlay systems. We also propose a variation of the problem by enforcing that each topic-connected overlay network be of constant diameter while keeping the average degree low. We present three heuristics for this problem that guarantee that each topic-connected overlay network will be of diameter 2 and that aim at keeping the overall average node degree low. Our experimental results validate our algorithms, showing that our algorithms are able to achieve very low diameter without increasing the average degree by much.

Efficient broadcasting and gathering in wireless ad-hoc networks

This paper considers the problem of broadcasting and information gathering in wireless ad-hoc networks, i.e. in wireless networks without any infrastructure in addition to the mobile hosts. Broadcasting is the problem of sending a packet from a source node in the network to all other nodes in the network. Information gathering is the problem of sending one packet each from a subset of the nodes to a single sink node in the network. Most of the proposed theoretical wireless network models oversimplify wireless communication properties. We use a model that takes into account that nodes have different transmission and interference ranges, and we propose algorithms in this model that achieve a high time and work-efficiency. We present algorithms for broadcasting a single or multiple message(s), and for information gathering. Our algorithms have the advantage that they are very simple and self-stabilizing, and would therefore even work in a dynamic environment. Also, our algorithms require only a constant amount of storage at any host. Thus, our algorithms can be used in wireless systems with very simple devices, such as sensors.

Distributed coloring in O/spl tilde/(/spl radic/(log n)) bit rounds

We consider the well-known vertex coloring problem: given a graph G, find a coloring of the vertices so that no two neighbors in G have the same color. It is trivial to see that every graph of maximum degree Delta can be colored with Delta + 1 colors, and distributed algorithms that find a (Delta + 1)-coloring in a logarithmic number of communication rounds, with high probability, are known since more than a decade. This is in general the best possible if only a constant number of bits can be sent along every edge in each round. In fact, we show that for the n-node cycle the bit complexity of the coloring problem is Omega(log n). More precisely, if only one bit can be sent along each edge in a round, then every distributed coloring algorithm (i.e., algorithms in which every node has the same initial state and initially only knows its own edges) needs at least Omega(log n) rounds, with high probability, to color the cycle, for any finite number of colors. But what if the edges have orientations, i.e., the end-points of an edge agree on its orientation (while bits may still flow in both directions)? Does this allow one to provide faster coloring algorithms? Interestingly, for the cycle in which all edges have the same orientation, we show that a simple randomized algorithm can achieve a 3-coloring with only O(radic(log n)) rounds of bit transmissions, with high probability (w.h.p.). This result is tight because we also show that the bit complexity of coloring an oriented cycle is Omega(radic(log n)), with high probability, no matter how many colors are allowed. The 3-coloring algorithm can be easily extended to provide a (Delta + 1)-coloring for all graphs of maximum degree Delta in O(radic(log n)) rounds of bit transmissions, w.h.p., if Delta is a constant, the edges are oriented, and the graph does not contain an oriented cycle of length less than radic(log n). Using more complex algorithms, we show how to obtain an O(Delta)-coloring for arbitrary oriented graphs of maximum degree Delta using essentially O(log Deltaradic(log n)) rounds of bit transmissions, w.h.p., provided that the graph does not contain an oriented cycle of length less than radic(log n)

Minimum Maximum Degree Publish-Subscribe Overlay Network Design

Designing an overlay network for publish/subscribe communication in a system where nodes may subscribe to many different topics of interest is of fundamental importance. For scalability and efficiency, it is important to keep the degree of the nodes in the publish/subscribe system low. It is only natural then to formalize the following problem: Given a collection of nodes and their topic subscriptions connect the nodes into a graph which has least possible maximum degree and in such a way that for each topic t, the graph induced by the nodes interested in t is connected. We present the first polynomial time logarithmic approximation algorithm for this problem and prove an almost tight lower bound on the approximation ratio. Our experimental results show that our algorithm drastically improves the maximum degree of publish/subscribe overlay systems. We also propose a variation of the problem by enforcing that each topic-connected overlay network be of constant diameter, while keeping the average degree low. We present a heuristic for this problem which guarantees that each topic-connected overlay network will be of diameter 2 and which aims at keeping the overall average node degree low. Our experimental results validate our algorithm showing that our algorithm is able to achieve very low diameter without increasing the average degree by much.

Parameterized maximum and average degree approximation in topic-based publish-subscribe overlay network design

Publish/subscribe communication systems where nodes subscribe to many different topics of interest are becoming increasingly more common. Designing overlay networks that connect the nodes subscribed to each distinct topic is hence a fundamental problem in these systems. For scalability and efficiency, it is important to keep the degree of the nodes in the publish/subscribe system low. Ideally one would like to be able not only to keep the average degree of the nodes low, but also to ensure that all nodes have equally the same degree, giving rise to the following problem: Given a collection of nodes and their topic subscriptions, connect the nodes into a graph with low average and maximum degree such that for each topic t, the graph induced by the nodes interested in t is connected. We present the first polynomial time parameterized sublinear approximation algorithm for this problem.We also propose a heuristic for constructing topic-connected networks with low average degree and diameter 2 and validate our results through simulations.

Brief announcement: parameterized maximum and average degree approximation in topic-based publish-subscribe overlay network design

Publish/subscribe communication systems where nodes subscribe to many different topics of interest are becoming increasingly more common. Designing overlay networks that connect the nodes subscribed to each distinct topic is hence a fundamental problem in these systems. For scalability and efficiency, it is important to keep the degree of the nodes in the publish/subscribe system low. Ideally one would like to be able not only to keep the average degree of the nodes low, but also to ensure that all nodes have equally the same degree, giving rise to the following problem: Given a collection of nodes and their topic subscriptions, connect the nodes into a graph with low average and maximum degree such that for each topic t, the graph induced by the nodes interested in t is connected. We present the first polynomial time parameterized sub linear approximation algorithm for this problem. We also propose two heuristics for constructing topic connected networks with low average degree and constant diameter and validate our results through simulations. In fact, the results in this section are a refinement of the preliminary results by Onus and Richa in INFOCOM’09.

Heuristics for minimum brauer chain problem

The exponentiation problem is computing xn for positive integer exponents n where the quality is measured by number of multiplications it requires. However, finding minimum number of multiplications is an NP-complete problem. This problem is very important for many applications such as RSA encryption and ElGamal decryption. Solving minimum Brauer chain problem is a way to solve the exponentiation problem. In this paper, five heuristics for approximating minimum length Brauer chain for a given number n is discussed. These heuristics are based on some greedy approaches and dynamic programming. As a result, we empirically get 1.1-approximation for the problem.