Hanjo Täubig

Technische Universität München | TUM · Department of Computer Science

Peer-to-peer systems rely on a scalable overlay network that enables efficient routing between its members. Hypercubic topologies facilitate such operations while each node only needs to connect to a small number of other nodes. In contrast to static communication networks, peer-to-peer networks allow nodes to adapt their neighbor set over time in...

We present a fast construction algorithm for the hierarchical tree decompositions that lie at the heart of oblivious routing strategies and that form the basis for approximation and online algorithms for various cut problems in graphs. Given an undirected graph G = (V, E, c) with edge capacities, we compute a single tree T = (Vt,Et,Ct), where the l...

We unify and generalize several inequalities for the number wkwk of walks of length kk in graphs, and for the entry sum of matrix powers. First, we present a weighted sandwich theorem for Hermitian matrices which generalizes a matrix theorem by Marcus and Newman and which further generalizes our former unification of inequalities for the number of...

Peer-to-peer systems rely on scalable overlay networks that enable efficient routing between its members. Hypercubic topologies fa- cilitate such operations while each node only needs to connect to a small number of other nodes. In contrast to static communication networks, peer-to-peer networks allow nodes to adapt their neighbor set over time in...

Proteins are among the most important organic compounds. The vast number of their functions are based on the specific effect of their various structures. To investigate the principles of protein structure and function experimentally determined structures were collected in the Protein Data Bank since 1971. Searching in this database is essential for...

In a recent article, Nadeem and Siddique used Chebyshev’s sum inequality to establish the Zagreb indices inequality M1/n ≤ M2/m for undirected graphs in the case where the degree sequence (di) and the degree-sum sequence (Si) are similarly ordered. We show that this is actually not a completely new result and we discuss several related results that...

In a recent article, Nadeem and Siddique used Chebyshev's sum inequality to establish the Zagreb indices inequality $M_1/n\le M_2/m$ for undirected graphs in the case where the degree sequence $(d_i)$ and the degree-sum sequence $(S_i)$ are similarly ordered. We show that this is actually not a completely new result and we discuss several related r...

We consider an undirected graph G with n vertices and m edges that is modified by introducing an intermediate vertex on every edge. It has been shown by Ilić and Stevanović that this subdivision graph SG satisfies the Zagreb indices inequality M1(SG)=(m + n)≤ M2(SG)=(2m). This inequality can also be expressed in the form w1(SG)≤ w2(SG)≤ w0(SG)≤ w3(...

Topological self-stabilization is an important concept to build robust open distributed systems (such as peer-to-peer systems) where nodes can organize themselves into meaningful network topologies. The goal is to devise distributed algorithms where nodes forward, insert, and delete links to neighboring nodes, and that converge quickly to such a de...

We investigate the growth of the number w_k of walks of length k in undirected graphs as well as related inequalities. In the first part, we deduce the inequality w_2a+c⋅w_2(a+b)+c ≤ w_2a⋅w_2(a+b+c), which we call the Sandwich Theorem. It unifies and generalizes an inequality by Lagarias et al. and an inequality by Dress and Gutman. In the same way...

Topological self-stabilization is an important concept to build robust open distributed systems (such as peer-to-peer systems) where nodes can organize themselves into meaningful network topologies. The goal is to devise distributed algorithms that converge quickly to such a desirable topology, independently of the initial network state. This pa- p...

This brief announcement proposes a new model to measure the distributed time complexity of topological self-stabilization. In the field of topological self-stabilization, nodes-e.g., machines in a p2p network—seek to establish a certain network structure in a robust manner (see, e.g., [2] for a distributed algorithm for skip graphs). While several...

This work draws attention to combinatorial network abstraction problems which are specified by a class \(\mathcal{P}\) of pattern graphs and a real-valued similarity measure \(\varrho\) based on certain graph properties. For fixed \(\mathcal{P}\) and \(\varrho\), the optimization task on any graph G is to find a subgraph G′ which belongs to \(\math...

PAST is a new web service providing fast structural queries of the Protein Data Bank. The search engine is based on an adaptation of the generalized suffix tree and relies on a translation- and rotation-invariant representation of the protein backbone. The search procedure is completely independent of the amino acid sequence of the polypeptide chai...

We contribute to the study of inferring commercial relationships between autonomous systems (AS relationships) from observable BGP routes. We deduce several forbidden patterns of AS relationships that impose a certain type of acyclicity on the AS graph. We investigate algorithms for solving the acyclic all-paths type-of-relationship problem, i.e.,...

We study the complexity of finding a subgraph of a certain size and a certain density, where density is measured by the average degree. Let gamma: N -> Q be any density function, i.e., gamma is computable in polynomial time and satisfies gamma(k) 0 and has a polynomial-time algorithm for gamma=2 O(1/k).

Among connected graphs, some are connected so slightly that removal of a Single Vertex or edge will disconnect them. Such vertices and edges are quite important. A vertex x is called a cutpoint in G if G − x contains more components than G does; in particular if G is connected, then a cutpoint is a vertex x such that G − x is disconnected. Similarl...

The first main goal of this paper is to present Sketch-it!, a framework aiming to facilitate development and experimental evaluation of new scheduling algorithms. It comprises many helpful data-structures, a graphical interface with several components and a library with implementations of selected scheduling algorithms. Every scheduling problem cov...

Abstract We study the complexity of nding a subgraph of a certain size and a certain density, where density is measured by the average degree. Let : N ! Q+ be any density function, i.e., is computable in polynomial time and satises (k) k 1 for all k 2 N. Then -Cluster is the problem of deciding, given an undirected graph G and a natural number k, w...

The first main goal of this paper is to present Sketch-it!, a framework aiming to facilitate development and experimental evaluation of new scheduling algorithms. It comprises many helpful datastructures, a graphical interface with several components and a library with implementations of selected scheduling algorithms. Every scheduling problem cove...

We study the complexity of finding a subgraph of a certain size and a certain density, where density is measured by the average degree. Let γ : ℕ → ℚ+ be any density function, i.e., γ is computable in polynomial time and satisfies γ(k) ≤ k − 1 for all k ∈ ℕ. Then γ-Cluster is the problem of deciding, given an undirected graph G and a natural number...