Christofides

Christofides is a surname of Greek origin. It is borne by several scholars, and in computer science it is closely associated with a well-known heuristic for the traveling salesman problem. The name is most often encountered in reference to the Christofides algorithm, which provides a guaranteed approximation for a class of TSP instances.

Christofides' algorithm addresses the metric traveling salesman problem, where distances are symmetric and satisfy the triangle inequality. The algorithm operates in polynomial time and yields a tour whose length is at most 1.5 times the optimum. The method proceeds as follows: first, compute a minimum spanning tree of the complete graph; second, identify the vertices of odd degree in the tree and compute a minimum-weight perfect matching among them; third, take the union of the tree and the matching to obtain an Eulerian multigraph; fourth, traverse an Euler tour and shortcut repeated vertices to form a Hamiltonian cycle, using the triangle inequality to ensure the length does not increase. The resulting tour is a feasible solution with the 1.5 bound, and the algorithm is constructive and widely used as a baseline in TSP research.

Beyond the algorithm, Christofides as a surname appears in academic contexts, but the algorithm remains the most prominent association in optimization literature. The technique illustrates how combining spanning trees, matchings, and Euler tours yields useful approximation guarantees for NP-hard problems.