Task: Solving a black-box graph combinatorial optimization problem via stochastic solution sampling following "heuristics".

I have 2 algorithms for this task.
The first algorithm and the corresponding code are:
<Algorithm description>: {alg_desc1}
<Code>: {alg_code1}
The second algorithm and the corresponding code are:
<Algorithm description>: {alg_desc2}
<Code>: {alg_code2}

Please help me create a new algorithm that is motivated by the given algorithms. Please provide a brief description of the new algorithm and its corresponding code. The `heuristics` function takes as input a matrix of edge attributes (shape: n by n) and a vector of node attributes (shape: n). A special node is indexed by 0. `heuristics` returns prior indicators of how promising it is to include each edge in a solution. The return is of the same shape as the input matrix of edge attributes. 

Your code description must start with ‘<start>’ and end with ‘<end>’. 
Your Python code should be formatted as a Python code string: "```python ... ```"

Be creative and do not give additional explanation.