@MISC{Presentation_theinteger, author = {The Following Presentation}, title = {The Integer Multicommodity Flow Problem}, year = {} }

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Abstract

+ (v) are the sets of arcs into and out of v, respectively. 3. demand: P e2ffi + (s i ) f i (e) d i . 4. integrality: all the flows f i (e) are integral. As stated above, the problem may be infeasible if the capacities available do not suffice to satisfy the demands. This lecture considers the integer multicommodity flow problem where we do not enforce any demand constraints, the flow shipped for any commodity is less or equal to 1, and the goal is to maximize the total flow over all commodities. 2 An LP-based approximation algorithm The integer multicommodity flow problem can be written as the following integer linear program (ILP). maxF = k X i=1 X e2ffi +