Abstract: A method for probabilistic lossy counting includes: for each element in a current window, determining whether an entry corresponding to a current element is present in a table; in the event an entry corresponding to the current element is present in the table, incrementing a frequency counter associated with the current element; otherwise, inserting an entry into a table, wherein inserting an entry comprises: calculating a probabilistic error bound ? based on an index i of the current window; and inserting the probabilistic error bound ? and a frequency counter into an entry corresponding to the current element in the table; and at the end of the current window, removing all elements from the table wherein the sum of the frequency counter and probabilistic error bound ? associated with the element is less than or equal to the index of the current window.

Abstract: A method of calculating a valley-free shortest path between two autonomous systems having a first graph representing an autonomous system topology and comprising a plurality of nodes and a plurality of links interconnecting the nodes, each link linking a first and a second node of the plurality of nodes. The method comprises generating a second graph using the first graph by: Mapping the nodes of the first graph into the second graph, by representing each node of the first graph by a respective uphill node and a downhill node; mapping each link of the first, second and third relationship type with a plurality of directed links between the uphill and downhill nodes according to the type of relationship. The method further comprises calculating the shortest-path route between two autonomous systems on the second graph, using the shortest-path routing algorithm.

Abstract: A method for determination of a network topology includes generating a list of device sets for a destination; removing any duplicate device sets from the list; creating a tree for the destination by introducing a root node into the tree; sorting the list of device sets for the destination by length; removing the shortest device set from the list; introducing a new node representing the shortest device set into the tree; determining whether a node in the tree represents a maximum length subset of the shortest device set, and in the event that a node is determined, connecting the new node to the determined node, or else connecting the new node to the root node; setting the identifier of the introduced node to a list of members of the shortest device set that are not included in the maximum length subset of the determined node.

Abstract: A method for determination of a network topology includes generating a list of device sets for a destination; removing any duplicate device sets from the list; creating a tree for the destination by introducing a root node into the tree; sorting the list of device sets for the destination by length; removing the shortest device set from the list; introducing a new node representing the shortest device set into the tree; determining whether a node in the tree represents a maximum length subset of the shortest device set, and in the event that a node is determined, connecting the new node to the determined node, or else connecting the new node to the root node; setting the identifier of the introduced node to a list of members of the shortest device set that are not included in the maximum length subset of the determined node.

Abstract: A method for probabilistic lossy counting includes: for each element in a current window, determining whether an entry corresponding to a current element is present in a table; in the event an entry corresponding to the current element is present in the table, incrementing a frequency counter associated with the current element; otherwise, inserting an entry into a table, wherein inserting an entry comprises: calculating a probabilistic error bound ? based on an index i of the current window; and inserting the probabilistic error bound ? and a frequency counter into an entry corresponding to the current element in the table; and at the end of the current window, removing all elements from the table wherein the sum of the frequency counter and probabilistic error bound ? associated with the element is less than or equal to the index of the current window.

Abstract: A method of calculating a valley-free shortest path between two autonomous systems having a first graph representing an autonomous system topology and comprising a plurality of nodes and a plurality of links interconnecting the nodes, each link linking a first and a second node of the plurality of nodes. The method comprises generating a second graph using the first graph by: Mapping the nodes of the first graph into the second graph, by representing each node of the first graph by a respective uphill node and a downhill node; mapping each link of the first, second and third relationship type with a plurality of directed links between the uphill and downhill nodes according to the type of relationship. The method further comprises calculating the shortest-path route between two autonomous systems on the second graph, using the shortest-path routing algorithm.