This work is a survey on a special minsum-maxmin bicriteria problem, known as the quickest path problem, that can model the transmission of data between two nodes of a network. Moreover, the authors review the problems of ranking the K quickest paths, and the K quickest loopless paths, and compare them in terms of the worst-case complexity order. The classification presented led to the proposal...

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We consider the problem of evaluating an expression consisting of unions and intersections of some sorted sets in the comparison model. Given the expression and the sizes of the sets, we are interested in the worst-case complexity of evaluating the expression in terms of the sizes of the sets. We assume the sets in the given expression are independent. We show a lower bound on this problem and ...

It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach to mitigate such concerns is the use of k-limited-access schemes [1], that restrict each client to learn only part of the index coding matrix, and in particul...

Three-color parity games capture the disjunction of a Büchi and a co-Büchi condition. The most efficient known algorithm for these games is the progress measures algorithm by Jurdziński. We present an acceleration technique that, while leaving the worst-case complexity unchanged, often leads to considerable speed-ups in games arising in practice. As an application, we consider games played in d...

We demonstrate that a resolution-r PR quadtree contaihing II points has, in the worst case, at most 8&r [log,(rt/2)]) + 8n/3 l/3 nodes. This captures the fact that as n tends towards 4’, the number of nodes in a PR quadtree quickly approaches O(n). This is a more precise estimation of the worst case space requirement of a PR quadtree then has been attempted before.

We give conditions under which the worst-case size of the silhouette of a polytope is sub-linear.

The star graph Sn has been recognized as an attractive alternative to the hypercube. Since S1; S2, and S3 have trivial structures, we focus our attention on Sn with n¿4 in this paper. Let Fv denote the set of faulty vertices in Sn. We show that when |Fv|6n− 5; Sn with n¿6 contains a fault-free path of length n! − 2|Fv| − 2 (n! − 2|Fv| − 1) between arbitrary two vertices of even (odd) distance. ...

In many application domains events are not Poisson distributed. For some applications it even makes sense to (more or less) assume that events are distributed in the worst possible way (e.g. in networks, packets often arrive in bursts). In this Section we study systems from a worst-case perspective. In particular, we analyze the price of not being able to foresee the future. This is a phenomeno...

For systems using software diversity, well-established theories show that the expected probability of failure on demand (pfd) for two diverse program versions failing together will generally differ from what it would be if they failed independently. This is explained in terms of a “difficulty function” that varies between demands on the system. This theory gives insight, but no specific predict...