E. Shargowitz and J. Keel. "A Global Router Based on Multicommodity Flow Model." The VLSI Journal, pp. 3--16, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by independently routing each net using the Lee Moore algorithm, and subsequently rerouting the overflow nets iteratively. Hu and Shing [2] extend the above algorithm as a hierarchical linear program and use column generating techniques to generate potential candidates. Several other approaches [3 6] model the global routing problem using a multicommodity flow paradigm. In [4] the routing problem is cast as a 0 1 multicommodity flow problem and solved approximately by first relaxing the 0 1 constraints to formulate a linear program, and then rounding off its non integral solution. Carden et ....

E. Shragowitz and S. Keel, A global router based on a multicommodity flow model, Integration, the VLSI Journal, vol. 5, pp. 3-16, 1987.

....are similar in the sense that they progress in time. That is, if a task loses an auction, it can use its money to win some other auction that will come along in the future. In the field of routing, there are some limited examples in the literature of economicbased strategies. For example [55] uses a multicommodity flow graph to first model the load with regard to various routing resources A cost function is then created to minimize the load. Because this cost function is created only after nets are routed to create a load, this method is in reality a sequential strategy. The above ....

E. Shragowitz and S. Keel. A global router based on a multicommodity flow model. INTEGRATION, the VLSI journal, 1987(5):3--16, 1987.

....Normalized Congestion 0 0.9 1 Slope = 0.01 Slope=10 Slope=100 Figure 7: Piecewise linear congestion cost function. As is done in a number of other routers we assign a congestion cost to each routing tile. A number of ways for modeling the congestion cost have been proposed in literature [21, 22, 23]. For the purpose of this work, we use a monotonic piecewise cost function of the type proposed in [24] see Figure 7) 4.2 Dynamic Edge Weights The cost of assigning a repeater to a CRB (or the edge cost) is a weighted composite function comprising of the congestion cost and the repeater block ....

E. Shragowitz and S. Keel, "A global router based on a multi commodity flow model," Integration, the VLSI Journal, vol. 5, pp. 3--16, Mar. 1987.

....there are few guarantees as to the quality of the resulting solution, or that the process will converge to a feasible solution. Despite these drawbacks, rip up and reroute continues to be used in many routing applications. The rip up and reroute portion of our global router is similar to that of [19], in that we iteratively change our congestion bounds to encourage convergence to a low congestion solution. In general, this approach can yield high quality results when given sufficient time and memory. Given the complexity of MCM and PCB designs, we believe that rip up and reroute may be ....

....each resource such that we find a relatively short path (in terms of wiring distance) while avoiding heavily congested areas. We are therefore interested in knowing what cost functions result in the best performance, a question that has received relatively little attention in the literature. In [19], the cost of routing in the most congested region is infinite, while the remaining regions have low cost. In [12] the cost of a routing path includes terms for the number of other routes that a path touches or crosses, as well as two terms to capture the route length in preferred and ....

[Article contains additional citation context not shown here]

E. Shragowitz and S. Keel. A global router based on a multicommodity flow model. Integration, the VLSI Journal, 5:3--16, 1987.

....and wire width changes. Our global router employs two basic routing engines for routing congestion optimization: one is based on the traditional rip up and reroute approach, and the other is based on iterative deletion. The rip up and reroute portion of our global router is similar to that of [60], in that we iteratively change the cost of each node in the routing graph based on the current congestion in that tilelayer so that the router tends to converge to a low congestion solution. The choice of routing cost functions and net routing orders was discussed in detail in [61] The iterative ....

E. Shragowitz and S. Keel, "A global router based on a multicommodity flow model," Integration, the VLSI Journal, vol. 5, pp. 3--16, 1987.

....and [7] which we extend to a vertex capacitated context. Section 4 describes a randomized rounding procedure that converts nearoptimal fractional MCF solutions to near optimal integral solutions. MCF based heuristics (with or without randomized rounding) have been applied to VLSI global routing [24, 3, 11]. However, global routing appears less naturally suited for MCF than our Global buffering problem; it does not seem to yield as strong theoretical bounds nor as effective implementations. Section 5 describes the four Global Buffering heuristics that we have implemented: i) Greedy, ii) e ....

E. Shragowitz and S. Keel, "A Global Router Based on a Multicommodity Flow Model", Integration 5(1) (1987), pp. 3--16.

.... even in the case of one bend routing of two terminal nets [4] For the routing problem in 2 D arrays, there have been various approaches based on hierarchical wiring [1] 3] 5] sequential methods [2] 4] 8] simulated annealing [10] linear programming [6] and multicommodity flow [9]. A quick heuristic is necessary for estimation of necessary wiring space and difficulty of routing in the early design planning stage. Consider the routing region with uniformly distributed pins. Then, it is often true that global density will be lower if we route the nets with less bends (even ....

E. Shargowitz and J. Keel, "A global router based on multicommodity flow model," Integration: The VLSI Journal, vol. 5, pp. 3--16, 1987.

.... even in the case of one bend routing of two terminal nets [4] For the routing problem in two dimensional arrays, there have been various approaches based on hierarchical wiring [1,3,5] sequential methods [2,4,8] simulated annealing [10] linear programming [6] and multicommodity flow [9]. A quick heuristic is necessary for estimation of necessary wiring space and difficulty of routing in the early design planning stage. Consider the routing region with uniformly distributed pins. Then, it is often true that global density will be lower if we route the nets with less bends (even ....

E. Shargowitz and J. Keel. "A Global Router Based on Multicommodity Flow Model". INTEGRATION: The VLSI Journal, 5:3-16, 1987.

.... be NP complete even in the case of one bend routing of two terminal nets [4] For the routing problem in two dimensional arrays, there have been various approaches based on hierarchical wiring [1, 3] sequential methods [7, 2] simulated annealing [11] linear programming [6] multicommodity flow [10] and flat approaches [4, 9] This paper is organized as follows. In Section 2, we define and formulate the problem. In Section 3, we obtain an approximate upper bounds for the worst case density of global cells needed to route nets using at most four bends per net. The bound is computed based on a ....

E. Shargowitz and J. Keel. "A Global Router Based on Multicommodity Flow Model". INTEGRATION: The VLSI Journal, 5:3--16, 1987.

.... nets [KLR 87] For the routing problem in two dimensional arrays, there have been various approaches based on hierarchical wiring [LST 87, BP83] sequential methods [LM84, Nai87, CSW90, LSW91] simulated annealing [VK83, KJV83] linear programming [NISV89, ML90] multicommodity flow [SK87, CC91] and flat approaches [KLR 87, SZ90] This paper is organized as follows. In Section 2, we define and formulate the problem. In Section 3, we introduce a global routing strategy based on top down recursion using 4 way partitioning (i.e. structured as a quad tree) Then, we obtain tight ....

E. Shargowitz and J. Keel. "A Global Router Based on Multicommodity Flow Model". INTEGRATION: The VLSI Journal, 5:3--16, 1987.

....both net topologies and cell positions may be affected. Linear programming methods have been used to select the assignment of segments in [2, 22] in order to minimize the maximum density across a channel. Related to the LP methods are those based on network flow or multicommodity flow models [30, 36, 7, 34]. In [20] the authors use path based timing constraints and utilize the features specific to bipolar design to optimize both the delay and area of the global routing result. The global router described in [16, 17] provides the basis for the work in this paper. It involves two phases, a ....

E. Shragowitz and S. Keel, "A Global Router Based on a Multicommodity Flow Model," Integration, j. 5, 1987, pp. 3-16.

....to the global routing problem; it generally requires long computation times and provides few guarantees as to solution quality. Despite these drawbacks, rip up and reroute continues to be used in many routing applications. The rip up and reroute portion of our global router is similar to that of [19], in that we iteratively change our congestion bounds to encourage convergence to a low congestion solution. Given the complexity of MCM and PCB designs, we believe that rip up and reroute may be necessary for aggressive design. We implement rip up and reroute in our router as follows. Each edge ....

....each resource such that we find a relatively short path (in terms of wiring distance) while avoiding heavily congested areas. We are therefore interested in knowing what cost functions result in the best performance, a question that has received relatively little attention in the literature. In [19], the cost of routing in the most congested region is infinite, while the remaining regions have low cost. In [12] the cost of a routing path includes terms for the number of other routes that a path touches or crosses, as well as two terms to capture the route length in preferred and ....

[Article contains additional citation context not shown here]

E. Shragowitz and S. Keel. A global router based on a multicommodity flow model. Integration, the VLSI Journal, 5:3--16, 1987.

....both net topologies and cell positions may be affected. Linear programming methods have been used to select the assignment of segments in [2, 22] in order to minimize the maximum density across a channel. Related to the LP methods are those based on network flow or multicommodity flow models [30, 36, 7, 34]. In [20] the authors use path based timing constraints and utilize the features specific to bipolar design to optimize both the delay and area of the global routing result. The global router described in [16, 17] provides the basis for the work in this paper. It involves two phases, a ....

E. Shragowitz and S. Keel, "A Global Router Based on a Multicommodity Flow Model," Integration, j. 5, 1987, pp. 3-16.

....absence of the minimization function, constraint (a) does not prohibit cycles on the connection path. However, under the assumption of positive edge costs, cycles are forbidden. This model interprets global routing as a multicommodity flow problem and was introduced before by one of the authors [SHR87 2]. 6 It should be noted that minimization of the connection length (or cost) is a primary goal only for nets with potential late arrival problems. For all other nets, all reasonable routes that satisfy the capacity constraints are acceptable. Shortest connections can themselves be a source of early ....

....if a connection cannot be found for the existing level of capacities, then the set of arcs with capacity 0 forms a cutset. Two approaches to this problem present themselves. The first is to re route previously routed connections and, by so doing, to decrease the number of elements in the cutset. [SHR87 2] describes a procedure of this type. The success of such a procedure in reducing a cutset to the extent that the searched for connection can be found is not guaranteed, while computational efforts may be quite substantial. Therefore, algorithm GR does not use this approach. The second possible ....

E. Shragowitz, J. Keel, "A Global Router Based on Multicommodity Flow Model," Integration, the VLSI Journal 5, pp.3-16, 1987.

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E. Shargowitz and J. Keel. "A Global Router Based on Multicommodity Flow Model." The VLSI Journal, pp. 3--16, 1987.

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E. Shragowitz and S. Keel, "A Global Router Based on a Multicommodity Flow Model", Integration 5(1) (1987), pp. 3--16.

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E. Shragowitz and S. Keel, "A global router based on a multicommodity flow model", Integration, 5 (1987), pp. 3--16.

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E. Shragowitz and S. Keel, "A global router based on a multicommodity flow model," Integration: the VLSI Journal, vol. 5, pp. 3--16, Mar. 1987.

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E. Shragowitz and S. Keel, "A global router based on a multicommodity flow model," Integration, the VLSI Journal, vol. 5, pp. 3-16, 1987.

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E. Shragowitz and S. Keel, "A Global Router based on a Multi Commodity Flow Model", Integration, the VLSI Journal, Vol. 5, pp. 3-16, 1987.

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