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

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

Please help me create a new function that is motivated by the given functions. Please provide a brief description of the new function and its corresponding code. The code function must be named 'heuristics'. The `heuristics` function takes as input a vector of node attributes (shape: n), a matrix of edge attributes (shape: n by n), and a constraint imposed on the sum of edge attributes. 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.