Apparatus and method for using and solving linear programming problem and applications thereof
First Claim
1. An apparatus configured to analyze a set of M inequalities constraints relating to N variables wherein M>
- N>
2, the apparatus comprising a memory; and
a processor configured by the memory to perform a method comprising the steps of;
(a) selecting a sub-set of R constraints wherein R>
N;
(b) calculating an Initial Feasible Region (IFR) defined by one or more endpoints and N constraints associated with each endpoints, wherein the endpoints are the intersections of the N constraints out of the selected sub-set, treated as equalities;
(c) selecting any first constraint out of the M constraints which is not part of the selected sub-set; and
(d) calculating a Temporary Feasible Region (TFR) by manipulating the IFR versus the first constraint.
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Abstract
Method and system for analyzing a linear programming problem or any other problem involving inequalities constraints set relating to multiple variables. An initial feasible region is calculated based on a sub-set of the constraints set. The feasible region is updated based on the additional constraints added one at a time. The method checks for feasibly, identifies active constraints, and provides end-points of the feasible region. The method may be applied to a control system or to a crossbar switch handling routing between multiple input and multiple outputs, such as digital data networking switch used to route TDM digital data streams being packet, frame or cell based, in a LAN, WAN, MAN or Internet application.
86 Citations
35 Claims
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1. An apparatus configured to analyze a set of M inequalities constraints relating to N variables wherein M>
- N>
2, the apparatus comprising a memory; and
a processor configured by the memory to perform a method comprising the steps of;(a) selecting a sub-set of R constraints wherein R>
N;(b) calculating an Initial Feasible Region (IFR) defined by one or more endpoints and N constraints associated with each endpoints, wherein the endpoints are the intersections of the N constraints out of the selected sub-set, treated as equalities; (c) selecting any first constraint out of the M constraints which is not part of the selected sub-set; and (d) calculating a Temporary Feasible Region (TFR) by manipulating the IFR versus the first constraint. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
- N>
-
20. A switching system based on a scheduling method, for use with a set of M inequalities constraints relating to N variables wherein M>
- N>
2, comprising;a memory for storing the scheduling method; a processor configured by the memory to perform the scheduling method; and a switch having a plurality of P input ports for receiving incoming streams and a plurality of Q output ports for outputting outgoing streams, the switch is configurable to be in multiple states, wherein in each state each of the input ports is connected to a single output port and each of the output ports is connected to a single input port for transferring the incoming streams into outgoing streams; wherein said switch is coupled to said processor for using said scheduling method as to determine the states'"'"' order and the length of stay in each state, and wherein said scheduling method comprising the steps of; (a) selecting a sub-set of L constraints wherein L>
N;(b) calculating an initial feasible region (IFR) defined by one or more endpoints and the N constraints corresponding to each endpoints, wherein the endpoints are the intersections of N constraints out of said selected sub-set, treated as equalities; (c) selecting a first constraint out of the M constraints which is not part of the selected sub-set; and (d) calculating a temporary feasible region (TFR) by manipulating the initial feasible region versus the first constraint. - View Dependent Claims (21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35)
- N>
Specification