Title: Feodor F. Dragan, Anh Tran and Chenyu Yan
1Network Flow Spanners
- Feodor F. Dragan, Anh Tran and Chenyu Yan
- Algorithmics Lab, Spring 2006, Kent State
University
EXAMPLE 2 denotes the capacity
3 denotes the price
In H, those 7 packages can be sent in two rounds
(52)
In G, we can send 7 packages from source to sink
at once
- OUR RESULTS
- The Light Flow-Spanner, Sparse Flow-Spanner,
Light-Edge-Connectivity-Spanner and Sparse
Edge-Connectivity-Spanner problems are
NP-complete. - The Light Tree Flow-Spanner problem is
NP-complete. - We give two approximation algorithms for the
Light Tree Flow-Spanner problem
- Our problems belong to the class of Network
Design and Network Survivability problems - They take into account Fault Tolerance, Bandwidth
Constraints and Link Failures
VARIATIONS OF LFSD
- RELATED WORK
- k-Edge-Connected-Spanning-Subgraph problem
- Given a graph G along with an integer k, one
seeks a spanning subgraph of G that is
k-edge-connected - MAX SNP-hard Fernandes98, (12/k)-approx.
algorithm Gabow et. al.05 - Original edge-connectivities are not taking into
account - Survivable-network-design problem (SNDP)
- Given a graph G(V, E), a non-negative cost p(e)
for every edge e?E and a non-negative
connectivity requirement rij for every
(unordered) pair of vertices i, j. One needs to
find a minimum-cost subgraph in which each pair
of vertices i, j is joined by at least rij
edge-disjoint paths. - NP-hard problem, 2(11/21/31/k)-approximation
algorithm Gabow et. al.98, Goemans et. al.94 - By setting rij?FG(i, j)/t? for each pair of
vertices i, j, our LECS problem can be reduced to
SNDP.
EXPERIMENTAL RESULTS
Experimental results for both approximation
algorithms
Experimental results on Internet-like graphs
Experimental results on random graphs
CONCLUSION The Light Tree t-Flow Spanner
approximation algorithm works better for small
stretch factors t while the Light Tree Flow
Spanner approximation algorithm works better for
larger t.
Results were partially presented at LATIN 2006
Conference, March 20-24, Valdivia, Chile