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For both the edge deletion heuristic and the maximum degree greedy heuristic, we study the problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r, where r is a fixed rational number. Our main results are that these problems are complete for the class of problems solvable via parallel access to NP. To achieve these...
We are given an undirected simple graph G = (V,E) with edge capacities , e ∈ E, and a set K ⊆ V2 of commodities with demand values d(s,t)εℤ, (s, t) ∈ K. An unsplittable shortest path routing (USPR) of the commodities K is a set of flow paths Φ(s,t), (s, t) ∈ K, such that each Φ(s,t) is the unique shortest (s, t)-path for commodity (s...
Some versions of the maximum common subgraph problem are studied and approximation algorithms are given. The maximum bounded common induced subgraph problem is shown to be Max SNP-hard and the maximum unbounded common induced subgraph problem is shown to be as hard to approximate as the maximum independent set problem. The maximum common induced connected subgraph problem is still harder to approximate...
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