TY - GEN

T1 - Counting Approximately-Shortest Paths in Directed Acyclic Graphs

AU - Mihalák, Matús

AU - Šrámek, Rastislav

AU - Widmayer, Peter

PY - 2013

Y1 - 2013

N2 - Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight l, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most l. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights l 1 and l 2, we show how to approximately count the s-t paths that have length at most l 1 in the first graph and length not much larger than l 2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph.

AB - Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight l, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most l. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights l 1 and l 2, we show how to approximately count the s-t paths that have length at most l 1 in the first graph and length not much larger than l 2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph.

U2 - 10.1007/978-3-319-08001-7_14

DO - 10.1007/978-3-319-08001-7_14

M3 - Conference article in proceeding

T3 - Lecture Notes in Computer Science

SP - 156

EP - 167

BT - Proc. 11th International Workshop on Approximation and Online Algorithms (WAOA)

PB - Springer Verlag

ER -