libsvm and liblinear are both software libraries that implement Support Vector Machines. What’s the
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In practice the complexity of the SMO algorithm (that works both for kernel and linear SVM) as implemented in libsvm is O(n^2) or O(n^3) whereas liblinear is O(n) but does not support kernel SVMs. n is the number of samples in the training dataset.
Hence for medium to large scale forget about kernels and use liblinear (or maybe have a look at approximate kernel SVM solvers such as LaSVM).
Edit: in practice libsvm becomes painfully slow at 10k samples.