Communication tree problems

In this paper, we consider random communication requirements and several cost measures for a particular model of tree routing on a complete network. First we show that a random tree does not give any approximation. Then give approximation algorithms for the case for two random models of requirements.Postprint (published version

A theory of flow network typings and its optimization problems

Many large-scale and safety critical systems can be modeled as flow networks. Traditional approaches for the analysis of flow networks are whole-system approaches in that they require prior knowledge of the entire network before an analysis is undertaken, which can quickly become intractable as the size of network increases. In this thesis we study an alternative approach to the analysis of flow networks, which is modular, incremental and order-oblivious. The formal mechanism for realizing this compositional approach is an appropriately defined theory of network typings. Typings are formalized differently depending on how networks are specified and which of their properties is being verified. We illustrate this approach by considering a particular family of flow networks, called additive flow networks. In additive flow networks, every edge is assigned a constant gain/loss factor which is activated provided a non-zero amount of flow enters that edge. We show that the analysis of additive flow networks, more specifically the max-flow problem, is NP-hard, even when the underlying graph is planar. The theory of network typings gives rise to different forms of graph decomposition problems. We focus on one problem, which we call the graph reassembling problem. Given an abstraction of a flow network as a graph G = (V,E), one possible definition of this problem is specified in two steps: (1) We cut every edge of G into two halves to obtain a collection of |V| one-vertex components, and (2) we splice the two halves of all the edges, one edge at a time, in some order that minimizes the complexity of constructing a typing for G, starting from the typings of its one-vertex components. One optimization is minimizing “maximum” edge-boundary degree of components encountered during the reassembling of G (denoted as α measure). Another is to minimize the “sum” of all edge-boundary degrees encountered during this process (denoted by β measure). Finally, we study different variations of graph reassembling (with respect to minimizing α or β) and their relation with problems such as Linear Arrangement, Routing Tree Embedding, and Tree Layout

Communication tree problems

In this paper, we deal with the problem of constructing optimal communication trees satisfying given communication requirements. We consider two constant degree tree communication models and several cost measures. First, we analyze whether a tree selected at random provides a good randomized approximation algorithm, and we show that such a construction fails for some of the measures. Secondly, we provide approximation algorithms for the case in which the communication requirements are given by a random graph in two different random models, namely the classical Gn,p and random geometric graphs. Finally, we conclude with some open problems

Communication tree problems

In this paper, we consider random communication requirements and several cost measures for a particular model of tree routing on a complete network. First we show that a random tree does not give any approximation. Then give approximation algorithms for the case for two random models of requirements

Communication Tree Problems ∗†

In this paper, we deal with the problem of constructing optimal communication trees satisfying given communication requirements. We consider two constant degree tree communication models and several cost measures. First, we analyze whether a tree selected at random provides a good randomized approximation algorithm, and we show that such a construction fails for some of the measures. Secondly, we provide approximation algorithms for the case in which the communication requirements are given by a random graph in two different random models, namely the classical Gn,p and random geometric graphs. Finally, we conclude with some open problems.