Richard B. Tan

Fundamental control algorithms in mobile networks

In this work we propose simple and efficient protocols for counting and leader election in mobile networks. For mobile networks with fixed base stations we provide a new and very efficient protocol for counting the number of mobile hosts. The main part of the work concentrates on ad-hoc networks (no fixed subnetwork). We provide a model for these networks and leader election (and a special form of counting) protocols for both named and anonymous mobile hosts. In this work we define two protocol classes, the NonCompulsoryprotocols, which do not affect the motion of the hosts and the Compulsory, which determine the motion of some or all the hosts. By assuming that the mobile hosts move as if each one is doing a continuous random walk on their allowable space S of motions, and by assuming a universal time, we show that our leader election protocol terminates (with high probability and also on the average) in time asymptotically linear to the size of the space S, measured as its volume divided by the volume of the sphere defined by the range of transmission of each mobile host. We also provide a simple but very efficient Compulsory (forced random walks) Las Vegas protocol for leader election in ad-hoc networks, which also allows counting, with termination detection. Our analysis techniques for the meeting time of concurrent random walks extend the known facts and are tight. They may be used as an analysis tool in the design of many other distributed protocols. This is the first algorithmic and characterization work, to our knowledge, for ad-hoc networks. *This work was partially supported by the EU ESPRIT LTR ALCOM-IT. (contract No. 20244). ‘Computer Technology Institute Kolokotroni 3, 26221 Patras, Greece. Email: {hatais,pentaris,spirakis,tampakas)bcti.gr ‘Computer Engineering and Informatics Department, Patras University, 26500 Rion. Patras. Greece. ‘Technological Educational Institute (TEI) of Patras, M Alexandrou 1, 26334, Koukouli, Patrss, Greece. ‘Universiteit Utrecht, Department of Computer Science, Centrumgebouw Noord, Padualaan 14, De Uithof, 3584 C4 Utrecht, The Netherlands. Email: rbtan&s.uu.nl Permission to make digital or hard copies of all or part of this work fix personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on sewers or to redistribute to lists. requires prior specific permission and/or a fee. SPAA ‘99 Saint Malo , France Copyright ACM 1999 l-581 13-124-0/99/06...

λ -Coloring of Graphs

5.00 Contact Author : George Pentaris, email pentorkOcti.gr

Channel assignment with separation for interference avoidance in wireless networks

A λ-coloring of a graph G is an assignment of colors from the set {0,....,λ} to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem.

Computer Networks with Compact Routing Tables

Given an integer /spl sigma/>1, a vector (/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/), of nonnegative integers, and an undirected graph G=(V, E), an L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers, such that |f(u)-f(v)|/spl ges//spl delta//sub i/, if d(u,v)=i, for 1<i<(/spl sigma/-1), where d(u, v) is the distance (i.e., the minimum number of edges) between the vertices u and v. An optimal L(/spl delta//sub 1/, /spl delta//sub 2/,..., /spl delta//sub /spl sigma/-1/)-coloring for G is one using the smallest range /spl lambda/ of integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e., colors) assigned to interfering stations (i.e., vertices) at distance i must be at least /spl delta//sub i/ apart, while the same channel can be reused in vertices whose distance is at least /spl sigma/. In particular, two versions of the coloring problem - L(2, 1, 1) and L(/spl delta//sub 1/, 1,..., 1) - are considered. Since these versions of the problem are NP-hard for general graphs, efficient algorithms for finding optimal colorings are provided for specific graphs modeling realistic wireless networks, including rings, bidimensional grids, and cellular grids.

Efficient use of radio spectrum in wireless networks with channel separation between close stations

The routing problem in computer networks is traditionally solved by providing detailed routing information for all destinations at every node. We consider the problem of routing messages with only a small amount of information at every node. For example, for every connected N-node network a scheme can be devised such that every message can be routed within O(√N) routing decisions. Improving on an observation of Santoro & Khatib [3] for trees we derive a general method of routing messages in arbitrary networks using tables of a size corresponding to the number of links at a node, while utilizing all links in the network.

Prefix routing schemes in dynamic networks

This paper investigates the problem of assigning channels to the stations of a wireless network so that interfering transmitters are assigned channels with a given separation and the number of channels used is minimized. Two versions of the channel assignment problem are considered which are equivalent to two specific coloring problems — called L(2, 1) and L (2, 1, 1) — of the graph representing the network topology. In these problems, channels assigned to adjacent vertices must be at least 2 apart, while the same channel can be reused only at vertices whose distance is at least 3 or 4, respectively. Efficient channel assignment algorithms using the minimum number of channels are provided for specific, but realistic, network topologies, including buses, rings, hexagonal grids, bidimensional grids, cellular grids, and complete binary trees.

An improved upperbound for distributed election in bidirectional rings of processors

Abstract We study a routing scheme on dynamic networks called the Prefix Routing scheme. The scheme is an abstraction of source routing. It assigns fixed addresses to the nodes of the network and one label per link. A message is routed by sending it out via the link with the maximum length (i.e., the “longest”) label that is a prefix of the address of the destination node. Arbitrary insertions of links and nodes are feasible with constant adaptation cost. It is shown that any dynamic growing network can be assigned a valid Prefix Routing scheme. We characterize completely the types of fixed networks with dynamic links (i.e., networks in which only the cost of the links can vary over time) and of dynamic networks with arbitrary insertions and deletions of nodes and links (without disconnecting the network) that allow optimum routing in this scheme. A hierarchy of so-called multi-label Prefix Routing schemes is presented. The connections between Prefix Routing and static Interval Routing are presented.

The derivation of graph marking algorithms from distributed termination detection protocols

We present a distributed algorithm for electing a leader (i. e., breaking symmetry) in bidirectional rings ofN processors with no global sense of orientation, that uses at most 1.44 ...N logN+O(N) messages in the worst case.

A Linear Kernel for the k-Disjoint Cycle Problem on Planar Graphs

Abstract We show that on-the-fly garbage collection algorithms can be obtained by transforming distributed termination detection protocols. Virtually all known on-the-fly garbage collecting algorithms are obtained by applying the transformation. The approach leads to a novel and insightful derivation of, e.g., the concurrent garbage collection algorithms of Dijkstra et al. and of Hudak and Keller. The approach also leads to several new, highly parallel algorithms for concurrent garbage collection. We also analyze a garbage collecting system due to Hughes from our current perspective.

Multidimensional interval routing schemes

We consider the following problem: given a planar graph G = (V,E) and integer k, find if possible at least k vertex disjoint cycles in G. This problem is known to be NP-complete. In this paper, we give a number of simple data reduction rules. Each rule transforms the input to an equivalent smaller input, and can be carried out in polynomial time. We show that inputs on which no rule can be carried out have size linear in k. Thereby we obtain that the k -Disjoint Cycles problem on planar graphs has a kernel of linear size. We also present a parameterized algorithm with a running time of