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تسجيل مستخدم جديدPolynomial Time $k$-Shortest Multi-Criteria Prioritized and All-Criteria-Disjoint Paths
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The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such attack over an edge, probabilities that can differ across edges. Furthermore, usage of a single shortest path (for routing) implies possible traffic bottleneck, which should be avoided if possible, which we term pathneck security avoidance. Finding all Pareto-optimal solutions for the multi-criteria single-source single-destination shortest secure path problem with non-negative edge lengths might yield a solution with an exponential number of paths. In the first part of this paper, we study specific settings of the multi-criteria shortest secure path problem, which are based on prioritized multi-criteria and on $k$-shortest secure paths. In the second part, we show a polynomial-time algorithm that, given an undirected graph $G$ and a pair of vertices $(s,t)$, finds prioritized multi-criteria $2$-disjoint (vertex/edge) shortest secure paths between $s$ and $t$. In the third part of the paper, we introduce the $k$-disjoint all-criteria-shortest secure paths problem, which is solved in time $O(min(k|E|, |E|^{3/2}))$.
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We study the decremental All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. The input to the problem is an $n$-vertex $m$-edge graph $G$ with non-negative edge lengths, that undergoes a sequence of edge deletions. The goal is
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Given a directed weighted graph $G=(V,E)$ undergoing vertex insertions emph{and} deletions, the All-Pairs Shortest Paths (APSP) problem asks to maintain a data structure that processes updates efficiently and returns after each update the distance ma
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A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process g
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