### Abstract

Original language | English (US) |
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State | Published - Jan 25 2005 |

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TY - PAT

T1 - Approximation Schemes for Finding a Path Subject to Many Additive Quality of Service Constraints

AU - Sen, Arunabha

AU - Xue, Guoliang

PY - 2005/1/25

Y1 - 2005/1/25

N2 - We study a computer network modeled by an edge weighted undirect graph G=(V,E), where V is the set of n vertices representing computers, E is the set of m edges representing communication links. Each edge e in E has K weights w1(e), w2(e),...,wk(e), where K is a constant greater than or equal to 2. wk(e) is called the kth weight of edge e. For a path p in the graph, the kth weight of the path, denoted by wk(p), is the sum of wk(e( over all edges e on path p.Given a source node s, a destination ode t and a set of K positive constratins W1, W2,..., Wk, the mulit-constrained QoS routing problem seeks to find an s-t path so that wi(p)0, find an approximate solution which is within a factor (1+epsilon) of the optimal solution, in time which is polynomial in n, m, and 1/epsilon.For the general case of K>=2, we present (1) an O(Km +n log n) time approximation alogrithm that guarantees a solution within a factor K of the optimal solution; (2) on O(m(n/epsilon)^(K-1)) time FPTAS; and (3) on O(n log n +m (H/epsilon)^(K-1)) time PTSAS when a feasible solution exists, where H is the minium hop count of any feasible path.Our results improve the stat of the arts when K is set to 2Compared to the method of Lorenz and Raz (reference 12 in paper in disclosure) the method is not only more general (K being any integer >=2), but also faster for K=2 in terms of time complexity: from O(m n(log log n+1/epsilon)) to O(m n (1/epsilon)).compared to the method fo Goel et al. (reference 6 in paper in disclosure), the method is not only more general (K being any integer>=2), but also faster for K-2 in terms of time complexity: from O((m+nlogn)H/Epsilon) to O(nlogn + mH/epsilon)

AB - We study a computer network modeled by an edge weighted undirect graph G=(V,E), where V is the set of n vertices representing computers, E is the set of m edges representing communication links. Each edge e in E has K weights w1(e), w2(e),...,wk(e), where K is a constant greater than or equal to 2. wk(e) is called the kth weight of edge e. For a path p in the graph, the kth weight of the path, denoted by wk(p), is the sum of wk(e( over all edges e on path p.Given a source node s, a destination ode t and a set of K positive constratins W1, W2,..., Wk, the mulit-constrained QoS routing problem seeks to find an s-t path so that wi(p)0, find an approximate solution which is within a factor (1+epsilon) of the optimal solution, in time which is polynomial in n, m, and 1/epsilon.For the general case of K>=2, we present (1) an O(Km +n log n) time approximation alogrithm that guarantees a solution within a factor K of the optimal solution; (2) on O(m(n/epsilon)^(K-1)) time FPTAS; and (3) on O(n log n +m (H/epsilon)^(K-1)) time PTSAS when a feasible solution exists, where H is the minium hop count of any feasible path.Our results improve the stat of the arts when K is set to 2Compared to the method of Lorenz and Raz (reference 12 in paper in disclosure) the method is not only more general (K being any integer >=2), but also faster for K=2 in terms of time complexity: from O(m n(log log n+1/epsilon)) to O(m n (1/epsilon)).compared to the method fo Goel et al. (reference 6 in paper in disclosure), the method is not only more general (K being any integer>=2), but also faster for K-2 in terms of time complexity: from O((m+nlogn)H/Epsilon) to O(nlogn + mH/epsilon)

M3 - Patent

ER -