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c_{j}=\epsilon_{2} |
\{e_{1},e_{2}\} |
\Delta_{2}({\text{MARK\_LEFT}})=(c_{1})\times X+(1-c_{1})\times X |
A |
S |
\alpha\geq 1 |
|w_{3}+w^{*}+w_{4}-w_{3}-w_{4}|=w^{*} |
\displaystyle\pi_{v_{i},u_{j}} |
\{v^{\prime}_{4},v^{\prime}_{5},v^{\prime}_{6}\} |
x=w_{0} |
v_{n_{1}+1} |
\displaystyle= |
e^{*}, |
{n_{L}}{n_{R}}\times(({\mathcal{L}}-i-1)({\mathcal{R}}-j)-({\mathcal{L}}-i)({%
\mathcal{R}}-j))={n_{L}}{n_{R}}\times({\mathcal{L}}{\mathcal{R}}-{\mathcal{L}}%
j-i{\mathcal{R}}+ij-{\mathcal{R}}+j-{\mathcal{L}}{\mathcal{R}}+{\mathcal{L}}j+%
i{\mathcal{R}}-ij)={n_{L}}{n_{R}}\times(j-{\mathcal{R}}) |
{R}_{j} |
-2\times R_{i}\times(S_{RM}-R_{i}) |
V_{m}=\{v|v,u\in V,\exists e=(u,v)\in E_{m}\} |
v_{2} |
\Delta_{v_{i},u_{j}}=\mathcal{E}^{v_{i},u_{j}}_{2}-\mathcal{E}^{v_{i},u_{j}}_{%
1}=\left|w^{*}_{k}\right|-\left|\mathcal{W}^{\prime}(E^{(v_{i},u_{j})})-%
\mathcal{W}^{*}(E^{(v_{i},u_{j})})\right|\leq\left|w^{*}_{k}-\mathcal{W}^{%
\prime}(E^{(v_{i},u_{j})})+\mathcal{W}^{*}(E^{(v_{i},u_{j})})\right| |
k |
w^{\prime}(e_{i})=w(e_{i})+\epsilon_{i},\epsilon_{i}\in\{0,w^{*}\} |
c_{1} |
n_{R}=3 |
\displaystyle=n_{L}\times(w_{0}-x+w_{0}+w_{1}-x+\dots+w_{0}+w_{1}+\dots+w_{k}-%
x)=n_{L}\times\big{(}\big{(}\sum_{j=0}^{k}(k+1-j)w_{j}\big{)}-(k+1)\times x%
\big{)} |
\mathcal{C}(v)=k |
\{v_{1},v_{2}\} |
\mathcal{E}_{L}^{(\frac{k}{2})} |
k^{\prime} |
c_{i}+c_{j}\leq 1 |
S_{L}-L_{i}-S_{R}\leq 0 |
\{v^{\prime}_{1},v^{\prime}_{2},v^{\prime}_{3}\} |
E^{\prime}\subset E |
v_{1},v_{3}\in\overline{V_{m}} |
w^{*}_{1},w^{*}_{2},\dots,w^{*}_{k} |
\mathcal{F} |
x<0 |
C\leq x\leq B+C |
T_{j}^{L} |
\mathcal{E}(M_{L}^{*})\leq\mathcal{E}(M_{R}^{*})\xrightarrow[]{}\sum_{e_{i}\in
E%
_{L}}L_{i}\times w^{*}\times(S_{L}-L_{i}-S_{R})\leq\sum_{e_{i}\in E_{R}}R_{i}%
\times w^{*}\times(S_{R}-R_{i}-S_{L}) |
x\geq A+B |
\mathcal{E}_{LR} |
\displaystyle\geq\mathcal{E}(M_{0})+\sum_{e_{i}\in E_{L}}L_{i}\times w^{*}%
\times(S_{L}-L_{i}-S_{R})=\mathcal{E}(M_{L}^{*}) |
x<w_{0} |
S_{RM}>0 |
\mathcal{E}(M)<\mathcal{E}(M^{\prime}) |
{L}_{i} |
{n_{R}} |
e_{1}=(v_{1},v_{3}) |
{\mathcal{L}}\xleftarrow[]{}|E_{L}| |
\mathcal{E}_{L} |
\mathcal{E}(M^{\prime\prime})\leq\mathcal{E}(M) |
w^{*} |
0<\epsilon<w_{\frac{k}{2}+1} |
|\sum_{k=i}^{n_{1}}\epsilon_{k}| |
|\Delta E| |
-R_{i}\times S_{LM} |
w^{\prime}(e)=w(e)+w(e^{*}) |
u_{1}\in T_{i}^{L},u_{2}\in T_{j}^{R} |
S_{RM}=0 |
\Delta({\text{MARK\_LEFT}})\leq 0 |
C_{R} |
-L_{i}\times(S_{LM})+L_{i}\times(S_{LU}-L_{i}) |
c_{0},c_{1},\dots,c_{i} |
k+1-j |
|\Delta E|\geq(n-2)B=|\overline{V_{m}}|B |
B\times k^{\prime}\times(n-(k+k^{\prime}))=B\times(n-2) |
P^{\prime} |
|\Delta E|^{\prime}\geq w^{*} |
C |
|y-C|+|y-B-C| |
E_{m}\subset E |
j<i+1 |
\overline{V_{m}}=V-V_{m} |
v_{i}\in V_{L},v_{i}\neq v_{n_{1}+1} |
{\mathcal{L}} |
e^{*}=(v_{1},v_{2}) |
y=C |
\mathcal{E}(M_{L}^{*})\leq\mathcal{E}(M_{R}^{*}) |
u\in T_{2}^{L} |
\Delta({\text{UNMARK\_RIGHT}}) |
v_{i},v_{j}\in V_{L}\;(i<j,\;j\neq n_{1}+1) |
c_{i}=1 |
{n^{2}_{R}}\times((j-1)({\mathcal{R}}-j+1)-j({\mathcal{R}}-j))={n^{2}_{R}}%
\times(j{\mathcal{R}}-j^{2}+j-{\mathcal{R}}+j-1-j{\mathcal{R}}+j^{2})={n^{2}_{%
R}}\times(2j-{\mathcal{R}}-1) |
\mathcal{C}(u)=k^{\prime} |
E^{\prime} |
0.4 |
\Delta({\text{UNMARK\_RIGHT}})=0 |
{n_{L}}{n_{R}}((i+1)j-ij)={n_{L}}{n_{R}}\times j |
-\left|w^{*}-\sum_{k=i}^{n_{1}}\epsilon_{k}\right| |
c_{i}<c_{j} |
e\in E^{\prime} |
k-k^{\prime}\geq 0 |
-R_{i}\times(S_{RU})+R_{i}\times(S_{RM}-R_{i}) |
w^{*}_{k} |
\operatorname{CONTRACTION}(\pi) |
T-\{v_{1},v_{2}\} |
V_{R} |
\begin{array}[]{cc}\Delta&=R_{i}\times\bigg{(}\underbrace{-(S_{RM}-R_{i})}_{<0%
}-S_{RU}\underbrace{-S_{LM}}_{<0}+S_{LU}\bigg{)}<R_{i}(\underbrace{-S_{RU}+S_{%
LU}}_{\leq 0})<0\end{array} |
G=P_{n} |
\triangleright |