在分散式系統中，資源配置是一個很重要的議題。已經有不少研究利用古典著 色問題將顏色視為資源來分配。本論文考量了在顏色數有所限制下的最小顏色 衝突數問題。除了允許節點可以與鄰近節點使用相同顏色之外，我們將著色問 題延伸為允許節點持有多重顏色。本論文以圖形壅塞賽理論為基礎提出了一個 可以在集中式控制模型下運行的分散式自我穩定著色演算法。此外，我們提出 此演算法在現行網路分散式系統中實作之可能性與挑戰，並改寫成可運行於行 動式隨意網路的協定。
本論文的模擬實驗分成三部分。實驗考慮了四種拓樸模型(UDG、ER model、
BA model 以及 WS model)。首先我們在保證能符合古典著色問題的情況下，模 擬了四個傳統的分散式自我穩定著色演算法以及我們所提出的最適回應和較適 回應之自我穩定著色演算法。實驗結果顯示我們的方法無論在何種拓樸邏輯中使 用的顏色數都高於傳統演算法，這是因為演算法設計的準則不同，我們的方法取 向於將所以可利用的顏色平均分配，而收斂時間則以我們的方法較為快速。第二 部分的模擬實驗則比較在限制顏色數的情況下，每個節點所持有的顏色數目造成 的影響。不管在何種拓樸邏輯，在可使用顏色數受限制的情形下，節點允許著色 數越高代表造成的衝突數越高，其中又以較適回應演算法的在顏色衝突數的表現 較優。這是因為較適回應演算法逐步搜索的解空間較為大，不易陷入區域最佳解，
因此通常可以獲得表現較佳的結果，但收斂時間也隨之增加。最適回應演算法則 在節點允許著色數增加到 2~3 時反而會加速其收斂時間。可以依據時間或是效能 的需求來做選擇本論文所提出的兩個方法。最後一個實驗則將本論文所提出的無 線網路協定模擬實作在現實環境中，網路中的節點在延後決策的過程中可以減少 不必要的訊息發送量以及降低進入區域最佳解的可能。
未來我們可以在最小顏色衝突問題中加入權重的考量，使顏色有著不同權 重，或者將節點的碰撞領域延伸為距離多少內會彼此造成干擾。如此一來可以
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將解決最小顏色衝數應用到現實生活中各式各樣的問題，例如應用在排程問題 中，分時多重進接(Time division multiple access; TDMA)中，主控者要如何分配 時間區塊給節點。在無線存取點選擇問題(AP selection problem)中，客戶要如何 去選擇適合的存取點。事實上自我穩定演算法在改寫成可實際應用的網路協定 仍有許多硬體層面會遇到的問題，例如節點的運算能力，MAC 層的路由協定等 等。本研究雖然在文中提出了一個可運行於行動式隨意網路的協定，之後仍可 以在實作方面作更進一步做改善。
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