The Maximum Degree-and-Diameter-Bounded Subgraph problem (MaxDDBS) is a problem in

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. Given a connected ''host graph G'', an

upper bound In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of . Dually, a lower bound or minorant of is defined to be an element of that is less ...

for the degree ''d'', and an upper bound for the

diameter In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest Chord (geometry), chord of the circle. Both definitions a ...

''k'', we look for the largest subgraph ''S'' of ''G'' with maximum degree at most ''d'' and diameter at most ''k''. This problem is also referred to as the Degree-Diameter Subgraph Problem, as it contains the

degree diameter problem In graph theory, the degree diameter problem is the problem of finding the largest possible graph (in terms of the size of its vertex set ) of diameter such that the largest degree of any of the vertices in is at most . The size of is boun ...

as a special case (namely, by taking a sufficiently large complete graph as a host graph). Despite being a natural generalization of the Degree-Diameter Problem, MaxDDBS only began to be investigated in 2011, while research in the Degree-Diameter Problem has been active since the 1960s. Regarding its computational complexity, the problem is

NP-hard In computational complexity theory, a computational problem ''H'' is called NP-hard if, for every problem ''L'' which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from ''L'' to ''H''. That is, assumi ...

, and not in

APX In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor a ...

(i.e. it cannot be approximated to within a constant factor in

polynomial In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...

time).

References

The MaxDDBS page in Combinatorics Wiki
* A.Dekker, H.Perez-Roses, G.Pineda-Villavicencio, and P.Watters. The Maximum Degree & Diameter-Bounded Subgraph and its Applications. Journal of Mathematical Modelling and Algorithms, 2012. DOI: 10.1007/s10852-012-9182-8 * M.Miller, H.Perez-Roses, and J.Ryan. The Maximum Degree and Diameter Bounded Subgraph in the Mesh. Discrete Applied Mathematics, 2012. DOI: 10.1016/j.dam.2012.03.035 Computational problems in graph theory {{graph-stub